Statistical Mechanics
Collective Alignment in LLM Multi-Agent Systems: Disentangling Bias from Cooperation via Statistical Physics
Cristiano De Nobili
We investigate the emergent collective dynamics of LLM-based multi-
agent systems on a 2D square
lattice and present a model-agnostic statistical-physics method to disentangle social conformity from intrinsic bias, compute critical exponents, and probe the collective behavior and possible phase transitions of multi-
agent systems. In our framework, each node of an $L\!\times\!L$
lattice hosts an identical LLM
agent holding a binary state ($+1$/$-1$, mapped to yes/no) and updating it by querying the model conditioned on the four nearest-neighbor states. The sampler temperature $T$ serves as the sole control parameter. Across three open-weight models (llama3.1:8b, phi4-mini:3.8b, mistral:7b), we measure magnetization and susceptibility under a global-flip protocol designed to probe $\mathbb{Z}_2$
symmetry. All models display temperature-driven order-disorder crossovers and susceptibility peaks; finite-size scaling on even-$L$
lattices yields effective exponents $\gamma/\nu$ whose values are model-dependent, close to but incompatible with the 2D Ising universality class ($\gamma/\nu=7/4$). Our method enables the extraction of effective $\beta$-weighted couplings $\tilde{J}(T)$ and fields $\tilde{h}(T)$, which serve as a measure of social conformity and intrinsic bias. In the models we analyzed, we found that collective
alignment is dominated by an intrinsic bias ($\tilde{h}\gg\tilde{J}$) rather than by cooperative neighbor coupling, producing field-driven crossovers instead of genuine phase transitions. These effective parameters vary qualitatively across models, providing compact collective-behavior fingerprints for LLM
agents and a quantitative diagnostic for the reliability of multi-
agent consensus and collective
alignment.
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Materials Science
Rare-Earth-Tuned Evolution from d- to f-Orbital Dominance and Giant Anomalous Hall Effect in Topological RGaGe (R = Ce, Pr, Nd) Semimetals
Zhian Xu, Jian Yuan, Ze Yan et al. (+4 more)
The family of noncentrosymmetric rare-earth germanides RGaGe (R = Ce, Pr, Nd) provides a rich materials platform to explore the intertwined physics of strong magnetism, electronic correlations, and topological band structures. Through a combination of
crystal growth, characterization, and first-principles calculations, we reveal that these compounds exhibit a pronounced uniaxial
magnetic anisotropy, leading to distinct ground states: RGaGe orders ferromagnetically with moments along the crystallographic c-axis, and shows an
antiferromagnetic-like structure in the ab-plane. A key finding is a significantly enhanced intrinsic anomalous
Hall conductivity (AHC) compared to their well-known RAlGe counterparts, which even reaches as high as 948 {\Omega}-1 cm-1 at 2 K in PrGaGe. Our theoretical analysis predicts that this AHC originates from a robust Weyl semimetallic state driven by inversion
symmetry breaking, where Weyl points near the
Fermi level couple strongly to the
magnetic order. Importantly, this topological state persists above the
magnetic ordering temperature, confirming its intrinsic electronic origin. Our calculation also reveals that, while the near-
Fermi-level states in CeGaGe and PrGaGe are dominated by d-orbital contributions, NdGaGe exhibits significant f-orbital involvement, signaling a progressive
evolution from d- to f-orbital dominated
topology. These results establish the RGaGe system as a tunable platform for systematically extending the RAlGe-related family, showcasing a large anomalous
Hall response and orbital
evolution near the
Fermi level, and advancing the understanding of the interplay between
topology and magnetism in
quantum materials.
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All authors Zhian Xu, Jian Yuan, Ze Yan, Xia Wang, Na Yu, Shihao Zhang, Yanfeng Guo
Statistical Mechanics · Cross-listed from math.NA
Mathematical analysis and numerical methods for the computation of transport coefficients in molecular dynamics
Noe Blassel, Louis Carillo, Shiva Darshan et al. (+7 more)
We review various numerical approaches to compute transport coefficients in molecular dynamics. These approaches can be broadly classified into three groups: (i) nonequilibrium methods based on applying an external driving field to the system, measuring the average response in the system, and evaluating the related linear response coefficient; (ii) approaches reformulating the transport coefficient of interest through a time correlation function for the
equilibrium dynamics (the most popular instances being Green–Kubo and Einstein formulas); (iii) transient techniques, where the transport coefficient can be computed by monitoring the return to the steady state of a dynamics perturbed off its stationary distribution. For all three classes of methods, we provide elements of numerical analysis, allowing to estimate or at least quantify the level of numerical errors in the
estimator of the transport coefficient; and also briefly present recent attempts to more efficiently compute transport coefficients with variance reduction approaches such as control variates, importance sampling and coupling methods. The computation of transport coefficients remains nonetheless challenging and will continue requiring research efforts in the foreseeable future.
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All authors Noe Blassel, Louis Carillo, Shiva Darshan, Raphael Gastaldello, Alessandra Iacobucci, Elisa Marini, Regis Santet, Xiaocheng Shang, Gabriel Stoltz, Urbain Vaes
Mesoscale and Nanoscale Physics · Cross-listed from quant-ph
Perspective on tailoring quantum coherence with electron beams
Nahid Talebi
Examining and controlling the interaction between
semiconductor quantum qubits and their environment can boost
semiconductor quantum technologies, which have many applications in table-top
quantum computing hardware. Electron beams in electron microscopes have opened up a new avenue for the
quantum-coherent probing of
semiconductor excitations and strong-coupling effects. Here, I provide a brief overview of recent advancements in electron-beam probes for investigating
quantum coherence in
semiconductors and two-dimensional materials, complemented by my perspective on using electron beams to manipulate the
entanglement and correlations between
quantum systems.
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Materials Science
Laser-induced demagnetization in a MAX phase (Cr0.5Mn0.5)2GaC
Iaroslav Mogunov, Artyom Gorshkov, Mikhail Rautskii et al. (+2 more)
Magnetic MAX phases are nanolaminated metals that combine ceramic-like thermal and mechanical stability with peculiar
magnetic ordering, making them attractive for thin-film optoelectronics and spintronics. However,
laser-induced magnetization dynamics in MAX phases remains largely unexplored. Here, we investigate
laser-induced ultrafast demagnetization in a 40-nm-thick epitaxial film of the
magnetic MAX phase (Cr0.5Mn0.5)2GaC, which magnetically orders below ~220 K, using time-resolved magneto-optical Kerr effect spectroscopy. We reveal, that the demagnetization transients exhibit a two-step type-II demagnetization, common for two-dimensional
magnetic systems. The second stage dominates the process and has a characteristic time of approximately 100 ps. Applying the three-temperature model, we extract the electron-
lattice,
spin-
lattice, and electron-
spin coupling constants. The reconstructed
spin heat capacity exhibits a weak temperature dependence, accounting for only a subtle slowing down of demagnetization at elevated temperatures and fluences.
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All authors Iaroslav Mogunov, Artyom Gorshkov, Mikhail Rautskii, Tatyana Andryushchenko, Alexandra Kalashnikova
Quantum Gases
Influence of pump size on pattern formation in exciton-polaritonic Bose-Einstein condensates in the non-Markovian regime
N. V. Kuznetsova, A. D. Alliluev, D. V. Makarov et al. (+1 more)
Dynamics of
exciton-polaritonic condensate under incoherent pumping is studied using the non-Markovian
stochastic Gross-Pitaevskii equation with the pseudo-differential dispersion term. This term corresponds to the lower energy branch of polaritons. It is shown that an increasing of the pumping spot area leads to the appearance of various spatial structures whose properties depend on the duration of the dynamical
memory. In the regime of short
memory time, condensate can form an extended state that spans outside the pumping area. We conclude that onset of such extended states is related to the specific form of the dispersion term causing the “traffic jam” effect. The case of long
memory time corresponds to enhanced condensate formation, when increasing of the pumping area leads to appearance of angular condensate structures which partially suppress emission of matter waves from the pumping area.
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All authors N. V. Kuznetsova, A. D. Alliluev, D. V. Makarov, A. A. Anisich
Disordered Systems and Neural Networks · Cross-listed from quant-ph
Quantum and classical processing with photonic quantum machine learning
J. C. López Carreño, S. Świerczewski, A. Opala et al. (+3 more)
Artificial intelligence and machine learning have been widely adopted both in the industry and in everyday life, but at the cost of high compute demands. Recent studies show that implementing machine learning in physical systems in the deep
quantum regime could not only lead to faster information processing, but also to perform tasks that are out of reach for classical systems. Here, we report a
quantum reservoir processing device capable of performing both
quantum and classical machine learning tasks. The implementation is realized with a programmable silicon chip excited with single
photons, a highly scalable and adaptable photonics technology. We successfully implement a variety of
quantum tasks, including
quantum state
tomography and measurement of
entanglement via negativity. Moreover, we implement a method of mitigation of experimental imperfections which results in a significant improvement in accuracy in comparison to the same system operating in the classical regime. Our results demonstrate a method to overcome a crucial bottleneck of
quantum technologies by providing a practical way of probing
quantum states.
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All authors J. C. López Carreño, S. Świerczewski, A. Opala, A. Salavrakos, B. Piętka, M. Matuszewski
Statistical Mechanics
Renormalization of Quantum Operations: Parity-Time Transition and Chaotic Flows
Atsushi Oyaizu, Hongchao Li, Masaya Nakagawa et al. (+1 more)
The renormalization group (RG) in statistical physics focuses on ground-state properties of
equilibrium systems. However, it is unclear how it should be generalized to nonunitary
quantum dynamics caused by dissipation and measurement backaction, in which the notion of conserved energy is absent. Here, we extend the RG to cover nonunitary
quantum dynamics governed by
quantum operations. By performing coarse-graining in real time, we find that the competition between decoherence and coherent dynamics plays a decisive role in the behavior of the RG flow. In particular, we find that chaotic behavior without fixed points emerges in the RG flow when coherent dynamics is dominant, with the parity-time transition serving as a prototypical example. The measurement-induced parity-time transition belongs to the universality class of the one-dimensional Yang-Lee edge singularity, which serves as a guide for experimentally realizing imaginary fields in
lattice spin systems with a
quantum system.
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All authors Atsushi Oyaizu, Hongchao Li, Masaya Nakagawa, Masahito Ueda
Materials Science · Cross-listed from cs.LG
QT-Net: Rethinking Evaluation of AI Models in Atomic Chemical Space
Pablo Martínez Crespo, Stefano Ribes, Martin Rahm et al. (+6 more)
Atomic properties such as partial charges or multipoles encode chemically meaningful information that can inform downstream molecular property prediction, but their evaluation as machine learning targets has been complicated by the absence of a principled out-of-distribution evaluation protocol at the atomic level. In this work, we propose a held-out evaluation protocol that clusters atomic environments by SOAP descriptors and computes metrics accounting only for cluster labels unseen during training. Following this procedure, we use 5$\times$5 cross-validation and Tukey's HSD to run a statistically rigorous comparison of E(3)-equivariant against non-equivariant, rotationally augmented models for predicting electron populations and multipoles of H, C, N, and O atoms. Building on our results, we introduce the
Quantum Topological Neural Network (QT-Net), a rotationally augmented, non-equivariant graph neural network. We show that QT-Net can be used to infer properties of atoms in molecules from QM9 outside our training set, and that these inferred properties can yield improvement when used as input features for downstream molecular property prediction. To further validate the framework, molecular dipole moments computed from QT-Net's per-atom outputs recover the ground-truth values reported in QM9. We release all code and data, including a JAX implementation of QT-Net, to support the broader use of learned QTA properties as inductive biases for atomic-scale molecular machine learning.
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All authors Pablo Martínez Crespo, Stefano Ribes, Martin Rahm, Richard Beckmann, Robert S. Jordan, Marisa Gliege, Santiago Miret, Vijay Kris Narasimhan, Rocío Mercado
Materials Science
Effective dynamic constants for nonequilibrium third-principles simulations
Mauro Pulzone, Iñigo Robredo-Magro and Jorge Íñiguez-González
Computational studies of the thermodynamic properties of materials at the mesoscopic and macroscopic scales – involving lengths and times of at least $\mu$m and $\mu$s, respectively – rely on a coarse-graining approximation such that only a few relevant collective variables are treated explicitly. Those variables typically take the form of fields defined everywhere in space or macroscopic quantities when spatial inhomogeneities can be treated implicitly. The free energy is usually expressed as a Landau-like potential whose temperature-dependent minima track stable states, characteristic
equilibrium fluctuations being implicitly accounted for. Further, the response of the system to external perturbations, and its relaxation toward thermal
equilibrium, are described in terms of simple equations of motion governed by effective inertial and viscous-damping constants. There is considerable literature on the problem of deriving Landau free energy potentials, from either experiment or predictive atomistic simulations, including recent efforts to develop systematic machine-learning approaches that we denote “third principles”. Much less
attention has received the calculation of the effective constants controlling the nonequilibrium macroscopic or mesoscopic dynamics. Here we tackle that problem, describing a protocol that allows us to compute the temperature-dependent inertial and damping coefficients associated to the electric polarization in representative soft-mode ferroelectric PbTiO$_{3}$. Our scheme lends itself to a widespread application, although the non-trivial behaviors found in PbTiO$_{3}$ suggest that more case studies will be needed to finetune a general and robust calculation protocol. Our results also allow us to comment on common assumptions in the literature of effective dynamic treatments of ferroelectrics and related materials.
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Quantum Gases
Bose-Fermi Mapping in Hubbard Models at Imaginary Chemical Potential and Phase-Induced Fermionization
Evangelos G. Filothodoros
We find a mapping between the attractive
Fermi-Hubbard model and the repulsive Bose-Hubbard model at finite temperature and at imaginary chemical potential $\mu =i\theta$. We show, by using a large $N$-expansion, that the partition functions of the two models are related by a simple shift $\theta \to \theta + \pi$. This condition maps the BCS–BEC crossover of attractive
fermions to a Bose–
Fermi crossover (
fermion-like occupation) of repulsive
bosons. Central feature of this correspondence plays the thermal kernel $g(\beta E,\phi),$ whose analytic continuation $g_B(\beta E,\phi) = g_F(\beta E,\phi+\pi)$ governs the bosonic and fermionic sectors. Interestingly, we are able to find that the special angles $\phi = 2\pi/3,4\pi/3$ for
fermions correspond to $\phi = \pi/3,5\pi/3$ for
bosons, marking the boundaries of a universal thermal window. We further argue that the present mechanism shows that fermionization can occur at finite interaction strength through a thermodynamic effect induced by the imaginary chemical potential. This suggests that it is a new way of fermionization (not a change in statistics but a
fermion-like behaviour) unlike the Tonks–Girardeau limit, where fermionization arises from an infinite repulsive interaction and anyonic or Floquet-engineered systems where transmutation emerges from modified statistics or dynamics. Essentially, the phase $\phi$ is a statistical parameter; by twisting the thermal phase, it generates
fermion-like behaviour without hard-core constraints or infinite repulsion but only by using thermodynamics. We derive the gap equation and number equation for the bosonic model, highlighting the role of the imaginary chemical potential as a statistical regulator. Our results provide a unified framework for understanding crossovers in interacting
lattice systems.
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Other Condensed Matter
Pulse, polarization and topology shaping of polariton fuids
Lorenzo Dominici, David Colas, Stefano Donati et al. (+9 more)
Here we present different approaches to ultrafast pulse and polarization shaping, based on a “
quantum fluid” platform of polaritons. Indeed we exploit the normal modes of two dimensional polariton fluids made of strong coupled
quantum well
excitons and microcavity
photons, by rooting different polarization and topological states into their sub-picosecond Rabi oscillations. Coherent control of two resonant excitation pulses allows us to prepare the desired state of the polariton, taking benefit from its four-component features given by the combination of the two normal modes with the two degrees of polarization. An ultrafast imaging based on the digital off-axis holography technique is implemented to study the polariton complex wavefunction with time and space resolution. We show in order coherent control of the polariton state on the Bloch sphere, an ultrafast polarization sweeping of the Poincaré sphere, and the dynamical twist of full Poincaré states such as the skyrmion on the sphere itself. Finally, we realize a new kind of ultrafast swirling
vortices by adding the angular momentum degree of freedom to the two-pulse scheme. These oscillating
topology states are characterized by one or more inner phase singularities tubes which spirals around the axis of propagation. The mechanism is devised in the splitting of the
vortex into the upper and lower polaritons, resulting in an oscillatory exchange of energy and angular momentum and in the emitted time and space structured photonic packets.
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All authors Lorenzo Dominici, David Colas, Stefano Donati, Galbadrakh Dagvadorj, Antonio Gianfrate, Carlos Sánchez Muñoz, Dario Ballarini, Milena De Giorgi, Giuseppe Gigli, Marzena H. Szymańska, Fabrice P. Laussy, Daniele Sanvitto
Disordered Systems and Neural Networks · Cross-listed from stat.ML
Sharp feature-learning transitions and Bayes-optimal neural scaling laws in extensive-width networks
Minh-Toan Nguyen and Jean Barbier
We study the information-theoretic limits of learning a one-hidden-layer teacher network with hierarchical features from noisy queries, in the context of knowledge transfer to a smaller student model. We work in the high-dimensional regime where the teacher width $k$ scales linearly with the input dimension $d$ – a setting that captures large-but-finite-width networks and has only recently become analytically tractable. Using a heuristic leave-one-out decoupling argument, validated numerically throughout, we derive asymptotically sharp characterizations of the Bayes-optimal generalization error and individual feature overlaps via a system of closed fixed-point equations. These equations reveal that feature learnability is governed by a sequence of sharp phase transitions: as data grows, teacher features become recoverable sequentially, each through a discontinuous jump in overlap. This sequential acquisition underlies a precise notion of effective width $k_c$ – the number of learnable features at a given data budget $n$ – which unifies two distinct scaling regimes: a feature-learning regime in which the Bayes-optimal generalization error $\varepsilon^{\rm BO}$ scales as $ n^{1/(2\beta)-1}$, and a refinement regime in which it scales as $n^{-1}$, where $\beta>1/2$ is the exponent of the power-law feature hierarchy. Both laws collapse to the single relation $\varepsilon^{\rm BO}=\Theta(k_c d/n)$. We further show empirically that a student trained with Adam near the effective width $k_c$ achieves these optimal scaling laws (up to a small algorithmic gap), and provide an information-theoretic account of the associated scaling in model size.
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Superconductivity
Exact Gaussian pinning of a relative-phase mode and interaction-driven detuning from the pinned frequency
Yogeshwar Prasad
Hybridization between two identical fermionic layers or components produces a rigid bonding–antibonding splitting $2t_h$. We show that in a paired state this scale enters the collective dynamics exactly within Gaussian fluctuation theory: the copy-odd relative-phase kernel vanishes at $\omega=2t_h$, with the underlying parity-pair identity holding pointwise in momentum. Within a broad class of conventionally paired systems, the result is independent of chemical potential, band structure, orbital content, and dimensionality. It follows from copy-pseudospin Larmor precession generated by intercopy hopping together with the Goldstone–Ward condition imposed by superconducting self-consistency. Pairing also isolates $2t_h$ from quasiparticle excitations, with thermal scattering below and pair creation above it whenever the gap is finite. At particle-hole
symmetry, where the copy-odd amplitude decouples, the kernel zero becomes an isolated relative-phase pole at $\Omega_L=2t_h$, and the layer-imbalance response is a single Gaussian mode exhausting its Gaussian first moment; the corresponding full-
Hamiltonian first moment obeys an exact operator sum rule. This pinning is not protected beyond Gaussian order. An exact interaction torque destroys the Larmor closure, while an exactly solvable rung and exact diagonalization of the attractive Hubbard model on a periodic $N_s=12$, $z=3$
bilayer honeycomb cluster show strong detuning. At $|U|=4t$, the dominant layer-imbalance excitation occurs at $0.467(2t_h)$ while retaining $98.6\%$ of the zeroth-moment spectral weight but only $92.4\%$ of the exact first moment. Thus the Gaussian result provides an exact reference frequency whose many-body renormalization can be substantial while a dominant layer-odd excitation survives.
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Statistical Mechanics · Cross-listed from hep-ph
Non-equilibrium scaling across first-order transitions with relativistic scalar fields
Leon J. Sieke, Jessica Fuchs and Lorenz von Smekal
We investigate the out-of-
equilibrium dynamics of a relativistic $Z_2$-symmetric scalar field theory with Langevin dynamics in two and three spatial dimensions under linear driving across
magnetic first-order phase transitions, close to and far below the critical temperature $T_c$. Using classical-statistical
lattice simulations, we find that if the driving timescale is sufficiently fast, the system exhibits finite-time scaling behavior independent of temperature and dimensionality, identical to that observed in mean-field simulations. In slow quenches near $T_c$ this mean-field behavior crosses over to critical Kibble-Zurek scaling behavior, while for temperatures $T \ll T_c$ nucleation and growth dominate the transition dynamics, resulting in corrections to scaling. Near the transition point where the order parameter changes sign, the crossover between mean-field and critical out-of-
equilibrium dynamics is found to be well described by the leading algebraic correction to Kibble-Zurek scaling. We find that universal non-
equilibrium scaling behavior can be observed for $T \lesssim T_c$, provided the driving is fast enough to avoid nucleation but slow enough for correlations to form, and compute the associated universal scaling functions for the order parameter.
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Materials Science
Strain-Enhanced Coherence in Curved hBN Quantum Emitters
Eyal Shoham, Sukanta Nandi, Ayelet Teitelboim et al. (+4 more)
Hexagonal boron nitride (hBN) hosts robust room-temperature single-
photon emitters, yet their coherence is typically limited by
phonon induced dephasing and spectral broadening. Here, we show that thermally induced
curvature in bulk like hBN flakes provides a strain enabled route to suppress defect
phonon coupling under ambient conditions. Nanoscale bubbles formed by thermal processing generate strong through thickness strain gradients, which we directly probe by infrared nano spectroscopy. These measurements reveal strain induced splitting of in-plane
phonon modes, evidencing a substantial local modification of the
phonon density of states.
Quantum emitters localized within these curved regions exhibit markedly enhanced room temperature spectral purity, with Debye Waller factors of 0.91 and narrower line widths than emitters in flat regions.
Photon correlation measurements confirm high-purity single
photon emission at room temperature. Supported by first-principles calculations, we attribute this behavior to strain driven
phonon redistribution, which depletes
phonons in tensile regions and accumulates them in compressive regions, thereby creating locally
phonon suppressed environments for defect emitters. These results establish strain engineering as an effective route for
phonon control in hBN and open a pathway toward high coherence, room-temperature
quantum light sources for integrated nano photonic platforms.
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All authors Eyal Shoham, Sukanta Nandi, Ayelet Teitelboim, Jeny Jose, Gil Atar, Ashwin Ramasubramaniam Tomer Lewi, Doron Naveh
Statistical Mechanics
Statistical mechanics of the $N$-queens problem
Zong-Yue Liu, Hai-Jun Liao and Lei Wang
We investigate the $N$-queens problem as a
lattice gas – a model in which $N$ queens are placed on an $N \times N$ chessboard with pairwise repulsive interactions along shared rows, columns, and diagonals – from the perspective of statistical mechanics. The ground states are exactly the $Q(N)$ solutions of the classical $N$-queens problem, with
entropy per queen $s_0 \approx \ln N - \gamma$ ($\gamma \approx 1.944$). This
entropy reflects a characteristic constraint hierarchy: each successive
geometric constraint – columns, then diagonals – reduces the
entropy from the free-placement value $\ln N$ by a definite constant. We derive the exact high-temperature energy $E/N \to 5/3$ as $N \to \infty$. Extensive Monte Carlo simulations with $10^8$ sweeps per temperature point for $N = 8$–$1024$ reveal that the specific heat per queen $C_v/N$ converges to a universal function of $T$ as $N \to \infty$. The converged curve features a non-divergent peak $C_v^{\max}/N \approx 1.63$ at $T^* \approx 0.235\,J$, establishing the absence of a thermodynamic phase transition. Combined with the trivially exact high-temperature
entropy $S(\infty)/N = (1/N) \ln \binom{N^2}{N}$, the convergence of $C_v/N$ enables a thermodynamic integration of $C_v/T$ from $T = \infty$ to $T = 0$ that recovers the ground-state
entropy – and hence the Simkin constant $\gamma$ – purely from Monte Carlo data. This provides an independent thermodynamic route to a fundamental combinatorial constant. Thermodynamic integration yields $\gamma_{\rm MC} = 1.946 \pm 0.003$ at $N = 1024$, within $0.1\%$ of the precise combinatorial value $\gamma = 1.94400(1)$. We further present a transfer-
matrix-based tensor network formulation that encodes the non-attacking constraints into a rank-9 site tensor with 17 nonzero elements, providing a complementary exact-enumeration route.
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Other Condensed Matter
Beyond Topological Invariants: Order Parameters from Dominant Fock-state Patterns
Tsz Hin Hui, Xiaodan Xia, Pedro D. Sacramento et al. (+1 more)
We introduce a general scheme for constructing order parameters (OPs) by extracting generic patterns from the dominant Fock states of many-body ground states. While topological phases are traditionally characterized by non-local invariants, we demonstrate that our real-space OPs provide a more refined classification. In the extended Su-Schrieffer-Heeger model, we show that the standard winding number is insufficient to fully distinguish all phases; our OPs reveal a hidden sub-structure where each topological sector splits into two distinct phases. Beyond identifying the phase boundaries, these OPs quantify the depth of a phase, and remain robust in characterizing transitions in disordered systems. Furthermore, our approach provides a practical finite-size diagnostic for the Berezinskii-Kosterlitz-Thouless transition in the interacting
spin-1/2 XXZ model. The presented framework offers a broadly applicable tool for uncovering the phase diagrams of diverse interacting and non-interacting
quantum many-body systems.
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All authors Tsz Hin Hui, Xiaodan Xia, Pedro D. Sacramento, Wing Chi Yu
Disordered Systems and Neural Networks
Partial annealing and pattern decorrelation in associative neural networks
Linda Albanese, Andrea Alessandrelli, Adriano Barra et al. (+2 more)
Using the Hopfield model as a
benchmark case, the present work focuses on the investigation of partially annealed associative neural networks, wherein neural dynamics is coupled to slowly evolving patterns within the two-temperature-two-timescale framework. This setting inherently introduces a real parameter n, reminiscent of the number of replicas in the celebrated replica trick, that tunes the separation of timescales and the effective interaction between fast (i.e. the
neurons) and slow (i.e. the synapses) degrees of freedom. By adapting Guerra's interpolation to the case, we derive the free energy without relying on analytical continuation. The obtained results demonstrate that negative values of n induce a progressive decorrelation of the stored patterns, thereby effectively reducing interference, promoting orthogonal configurations and ultimately conferring to the network the maximal storage alphac=1. Numerical simulations based on a mean field Monte Carlo dynamics have been employed to confirm this scenario and prove that partial annealing restores
retrieval in challenging regimes, such as in the presence of biased patterns, outperforming standard decorrelation methods. These findings underscore the notion of partial annealing as an adaptive mechanism for enhancing
memory organisation and
retrieval in complex systems.
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All authors Linda Albanese, Andrea Alessandrelli, Adriano Barra, Silvio Franz, Federico Ricci-Tersenghi
Quantum Gases
Floquet-tuned superfluid-checkerboard competition in dipolar bosons
Jin Yang, Yaghmorassene Hebib and Chao Zhang
We study hard-core dipolar
bosons on a square
lattice subject to a unidirectional periodic drive that Floquet-engineers anisotropic hopping. Driving along one
lattice direction provides a controlled way to suppress transverse tunneling, yielding a kinetically quasi-one-dimensional regime with strongly anisotropic transport within the leading-order high-frequency Floquet effective description. In this limit, the system does not reduce to decoupled chains, due to the long-range in-plane dipolar interaction remains isotropic and couples different chains. Focusing on dipoles polarized perpendicular to the plane, for which the interaction is purely repulsive and isotropic, we use sign-problem-free worm-
algorithm quantum Monte Carlo simulations to map the half-filling phase diagram versus kinetic anisotropy and dipolar coupling. We find that increasing kinetic anisotropy systematically lowers the interaction strength required to stabilize checkerboard order, demonstrating that Floquet-induced suppression of transverse motion enhances density ordering. Near the superfluid–checkerboard boundary, finite-size results reveal a narrow transition region where the stiffness drops rapidly while checkerboard correlations rise sharply; Its pronounced sharpening with system size is consistent with a weakly first-order transition rounded by finite-size effects. Away from half filling, on the doped sides of the checkerboard plateau, we identify a narrow checkerboard-supersolid regime with simultaneously finite checkerboard correlations and superfluid stiffness, where the superfluid stiffness is anisotropic but the density pattern is isotropic.
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Materials Science
Saddle-node bifurcation in interfacial morphology selects battery degradation phase
Changdeuck Bae
We propose a minimal nonlinear closure ODE for the dynamic active-area factor of a battery interface and show that it exhibits a saddle-node bifurcation when the smoothing rate saturates with surface roughness. The closure is the simplest physically motivated extension of a recently introduced single-fixed-point closure [C. Bae, in preparation (2026)]: u = K - u/(1 + alphau^2), where u = xi - 1 is the dimensionless excess active area, K the dimensionless drive, and alpha a single saturation parameter. The bifurcation occurs at K_c = 1/(2sqrt(alpha)), separating a smooth passivating phase from a morphologically unstable phase. Mapping four canonical anode configurations – graphite, silicon composite, lithium metal, and anode-free Li/Cu – onto the closure via end-of-cycling steady-state xi extracted from publicly available long-cycle data populates the stable branch with monotonically increasing K/K_c ratios: graphite (~0.01), silicon composite (~0.24), lithium metal (~0.73), and anode-free (~0.95). The anode-free configuration sits within 5% of the saddle-node threshold, predicting a vanishingly small operational stability window in current density, temperature, and electrolyte composition. We test three falsifiable predictions of the framework – a critical current density, a critical temperature shift, and a mean-field critical-slowing-down exponent – and find them broadly consistent with publicly available data. We argue that this near-critical position is universal to nucleation-controlled deposition on non-passivating substrates.
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Quantum Gases
Local supersolid in moiré modulated Bose-Hubbard model using density-matrix renormalization group method
Siyu Xie, Qiang Xu, Qianqian Shi et al. (+1 more)
The search and characterization of supersolid phases remain a central topic in condensed matter physics. Inspired by the experimental discovery of local superfluid and insulating phases in two-dimensional moiré optical
lattices [Meng et al., Nature 615, 231 (2023)], we systematically explore the emergence of a local supersolid ($l$SS) phase in a one-dimensional Bose-Hubbard model subjected to a moiré potential, using the density-
matrix renormalization group method. We impose a maximum site occupation $n_{\rm max}=2$ to realize the soft-core
boson constraint. In the absence of nearest-neighbor repulsion, we identify the conventional superfluid, local superfluid, Mott
insulator, and moiré-induced
insulator phases. When the nearest-neighbor repulsion is turned on, the $l$SS phase emerges in the strong-moiré regime. This phase is uniquely characterized by three key signatures: (i) coexisting local staggered density order and local off-diagonal coherence within isolated moiré supercells; (ii) exponentially decaying global off-diagonal correlations; and (iii) a vanishing global structure factor in the thermodynamic limit, while the local structure factor remains finite. These features clearly distinguish the $l$SS from the conventional global supersolid (SS) phase, which exhibits algebraic correlations and a finite global structure factor. Our results provide a complete microscopic picture of local
quantum phases in moiré
lattices and offer clear experimental observables for detecting $l$SS states with ultracold atoms.
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All authors Siyu Xie, Qiang Xu, Qianqian Shi, Wanzhou Zhang
Strongly Correlated Electrons · Cross-listed from hep-th
Bulk-Edge Correspondence via Higher Gauge Theory
Hisham Sati and Urs Schreiber
More profound than bulk topological order of
quantum materials is only its unwinding via gapless excitations along boundaries of the sample. We recast this bulk-edge correspondence – for the experimentally relevant case of fractional
quantum Hall (FQH) systems – in terms of effective relative higher gauge theory, controlled by choices of classifying fibrations. For FQH systems, we identify the complex
Hopf fibration as classifying the bulk/boundary topological effects, and find that it yields a non-Lagrangian reconstruction of Floreanini-Jackiw/Wess-Zumino-Witten
chiral edge currents. Remarkably, the resulting effective FQH higher gauge theory turns out to be "geometrically engineered" on M2/M5-branes probing A-type orbi-singularities in 11D supergravity, globally completed by flux-quantization in twisted equivariant differential (TED) Cohomotopy: Here the M-string ends of M2-branes on M5-branes engineer the FQH
liquid's boundary. This
geometric engineering on M-branes might naturally elucidate the curious combination of $W_\infty$-
symmetry and of super-
symmetry that is known to govern the collective excitations of FQH
liquids at long wavelengths.
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Superconductivity
Apparent double-$T_c$ from a single BKT transition in anisotropic phase-only models
Pei-Yuan Cai and Yi Zhou
Transport experiments on two-dimensional
superconductors often yield direction-dependent transition temperatures, raising the question of whether such a “double-$T_c$” reflects a true thermodynamic splitting or a transport artifact. To establish a baseline, we study a minimal anisotropic phase-only Josephson-junction array in
equilibrium and under resistively shunted junction dynamics with fluctuating twist boundary conditions. The
equilibrium model exhibits a single Berezinskii–Kosterlitz–Thouless (BKT) transition. Out of
equilibrium, anisotropic Josephson couplings and anisotropic dissipation reshape the linear $R$–$T$ curves in a finite-size, finite-current crossover regime, so that curve-shape criteria such as Halperin–Nelson fits and fixed-resistance thresholds yield an apparent double-$T_c$. In contrast, critical-scaling criteria – the universal exponent $\alpha=3$ and dynamic finite-size scaling – remain consistent with the single $T_{\mathrm{BKT}}$. A robust splitting that persists in the nonlinear critical scaling, such as that recently reported at KTaO$_3$ interfaces, therefore points to physics beyond this clean anisotropic baseline.
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Materials Science
Parabolic-growth universality and its nucleation-driven breakdown across lithium-battery anode chemistries
Changdeuck Bae
Solid-electrolyte interphase (SEI) growth is widely modeled
cell-by-
cell with chemistry-specific closures, yet its underlying kinetic scaling is rarely tested across chemistries. By compiling cycle-resolved data from public long-cycle
datasets covering four anode configurations – graphite, silicon composite, lithium metal, and anode-free – we show that the cumulative interphase-loss index Lambda_int obeys the
parabolic law Lambda_int = A_chem * sqrt(1 - Theta_Li) in three of the four chemistries, with an exponent indistinguishable from alpha = 1/2 within experimental uncertainty. The chemistry-specific prefactor A_chem spans an order of magnitude, but the
diffusion-limited
parabolic kinetics is preserved. The fourth chemistry, anode-free configurations, deviates with a super-
parabolic exponent alpha approx 0.77, consistent with a nucleation-controlled growth regime. We rationalize the result using the Tammann-Deal-Grove
parabolic-growth framework adapted to interphase formation and identify the conditions under which universality is recovered. The observed regularity reduces SEI modeling complexity to a single rate constant per chemistry and provides a sharp falsifiable test for next-generation
cell formats.
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Mesoscale and Nanoscale Physics
One-dimensional relativistic hydrogen-like atom in Dirac materials: Energy spectra and supercritical states
S.Z. Rakhmanov, K.P. Matchonov, A.K. Rakhimov et al. (+1 more)
We consider a model of 1D relativistic hydrogen-like atom, formed by a Coulomb
impurity in
graphene nanoribbon. Describing the electron motion in terms of the one-dimensional Dirac equation for Coulomb potential taking into account the finite-size of the atomic
nucleus, we compute the
eigenvalues and eigenfunctions of the atomic electron. The cases of unconfined atom and atomin-box system are considered. Special focus is given calculation of supercritical energy levels and the critical charge. The latter is the value of the atomic
nucleus charge, when the electronic state reaches the border of the Dirac sea. It is found that for confined atom the value of the critical charge is larger than that of free atom. Experimentally measurable characteristics, local density of states is also plotted for both cases. Existence of strong localization for atom-in-box system is shown.
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All authors S.Z. Rakhmanov, K.P. Matchonov, A.K. Rakhimov, D.U. Matrasulov
Statistical Mechanics
Computing eigenpairs of quantum many-body systems with Polfed.jl
Rok Pintar, Konrad Pawlik, Rafał Świętek et al. (+5 more)
We present Polfed$.$jl, an open-source Julia package implementing the Polynomially Filtered Exact Diagonalization (POLFED)
algorithm for computing mid-spectrum
eigenvalues and eigenvectors (shortly, eigenpairs) of
quantum many-body
Hamiltonians. Access to such eigenpairs is essential for studying non-
equilibrium many-body physics, but is hindered by the exponential growth of
Hilbert-space dimension. POLFED addresses this challenge through a
polynomial spectral transformation evaluated on the fly within a Lanczos iteration, preserving
Hamiltonian sparsity and substantially reducing
memory costs compared to other diagonalization methods. The package supports flexible energy targeting, automatic optimization of the spectral mapping for structured
Hamiltonians, and GPU acceleration, which is particularly effective since the dominant computational cost reduces to repeated sparse
matrix-vector multiplications.
Benchmarks on disordered
spin-chain and fermionic models demonstrate access to larger system sizes than alternative approaches, and CPU–GPU comparisons confirm significant speedups. In particular, we also provide code for constructing the
quantum sun model
Hamiltonian, a toy model of a many-body ergodicity-breaking transition. While our focus is on many-body
Hamiltonians, Polfed$.$jl may be applied to any large sparse
matrix.
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All authors Rok Pintar, Konrad Pawlik, Rafał Świętek, Miroslav Hopjan, Jan Šuntajs, Jakub Zakrzewski, Piotr Sierant, Lev Vidmar
Materials Science
Non-homogeneous structure of complex concentrated alloys: Effect of intrinsic strain
Vaclav Paidar, Pavel Lejcek and Andrea Skolakova
Even if the atoms of a multicomponent
alloy occupy a common
lattice, their distribution is not homogeneous, and regions with different compositions can be detected. Three representative examples will be discussed: a Cantor-type system containing transition-metal elements (Cr, Mn, Fe, Ni, and Co), a refractory high-
entropy alloy (Ti, Zr, Nb, Ta, and Mo), and a multicomponent system combining transition and refractory metals (Cu, Ni, Ti, Zr, and Hf). Using a combination of theoretical analysis and experimental observations, we demonstrate that the formation of locally segregated regions can lead to a reduction in the overall energy of the system. This stabilization arises from the compensation of tensile and compressive strain fields associated with atoms of different sizes, highlighting the key role of local chemical and structural heterogeneity in determining the thermodynamic stability of multicomponent
alloys.
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Materials Science
Ytterbium charge state and stabilization in the Ba(Ca)F$_2$ host by electron paramagnetic resonance and infrared photoluminescence
David John, Shelja Sharma, Marius Stef et al. (+18 more)
Lanthanide-doped fluorides are promising materials for advanced photonic and
quantum applications due to their wide bandgap, low
phonon energy, and chemical stability. In this work, we present a systematic comparative study of ytterbium incorporation at low doping levels (0.05–0.2 mol%) in BaF$_2$ and CaF$_2$ single
crystals, focusing on the interplay between host
lattice properties, charge-state stabilization, and defect formation mechanisms. Using a combination of X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), electron paramagnetic resonance (EPR), transmittance, and infrared photoluminescence (IR PL), we explore how host
lattice properties affect the stabilization of Yb$^{3+}$ and Yb$^{2+}$ ions. XRD confirmed cubic phase purity and
lattice parameter stability in both hosts, while XPS revealed surface chemical composition variations associated with charge-compensating defects and trace
impurities. EPR spectra indicated that BaF$_2$ favored perturbed Yb$^{3+}$ environments with increasing dopant levels, while CaF$_2$ maintained predominantly unperturbed sites, suggesting a more favorable ionic match for Yb$^{2+}$. Photothermal deflection spectroscopy (PDS) and IR PL results showed host-specific optical responses, with CaF$_2$ exhibiting
crystal-field splitting and broader local field effects. These results reveal a clear decoupling between long-range structural stability and local
lattice perturbations, and demonstrate that host cation identity governs the balance between Yb$^{2+}$ and Yb$^{3+}$ stabilization as well as defect-driven optical behavior. This offers valuable insights for optimizing rare-earth-doped fluoride
crystals in
laser, scintillator, and
quantum device applications.
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All authors David John, Shelja Sharma, Marius Stef, Gabriel Buse, Zdeněk Remeš, Anna Artemenko, Sergii Chertopalov, Vineet Sikarwar, Alan Mašláni, Jafar Fathi, Jakub Pilař, Tomáš Hostinský, Jan Zich, Tomáš Mates, Brenda Natalia Lopez Nino, Michal Hlína, Karol Bartosiewicz, Marina Konuhova, Anatoli Popov, Ján Lančok, Maksym Buryi
Mesoscale and Nanoscale Physics
Cascade of fractional quantum Hall states in 2D system
Zhimou Chen, Jiaojie Yan, Yuxuan Zhu et al. (+11 more)
The observation of the fractional
quantum Hall (FQH) effect in 2D electron gases ushered in investigations of topological phases driven by strong electron correlations. Their remarkable features include fractionalized elementary excitations, gapless boundary states, and non-trivial
quantum entanglement patterns. Thanks to persistent efforts in the building of new platforms and making higher-quality samples, a diverse plethora of FQH states have been unveiled in experiments. We report a systematic study of ultrahigh-quality GaAs/AlGaAs
quantum wells with mobility up to 3.7*10^7 cm^2/V/s using
quantum transport measurements in
nuclear adiabatic demagnetization and dilution refrigerators down to 1 mK. In addition to many FQH states that have already been identified in previous work, new longitudinal resistance dips are observed at filling factors 17/33 and 15/31. The application of an in-plane
magnetic field causes disparate variations of the FQH states. The theoretical foundation of these states is discussed in the framework of composite
fermion theory. While most fractions can be explained as non-interacting composite
fermions forming integer
quantum Hall states, a few states correspond to FQH states of composite
fermions that arise from residual interaction between them. We summarize the observed fractions in the range of 0 < {\nu} < 2 and propose a pattern to account for their experimental appearance that provides an intuitive picture about the relative strengths of different FQH states.
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All authors Zhimou Chen, Jiaojie Yan, Yuxuan Zhu, Zhe Cui, Loren N. Pfeiffer, Kenneth W. West, Kirk W. Baldwin, Adbhut Gupta, Yang Liu, Wei Zhu, Wenchen Luo, Ying-Hai Wu, Shuai Yuan, Xi Lin