Papers

Recent years have witnessed substantial progress in the entanglement-based characterization of quantum phases of matter, with growing interest in real-space formulas due to their theoretical and experimental relevance. For two-dimensional gapped quantum systems, we propose a universal real-space formula for the chiral central charge based on the twist-operator correlator $Z_{g,h}=\langle\psi^{(N)}\rvert\mathcal{T}_A(g)\mathcal{T}_B(h)\mathcal{T}_C(g)\mathcal{T}_C(h)\lvert\psi^{(N)}\rangle$, where $\lvert\psi^{(N)}\rangle=\lvert\psi\rangle^{\otimes N}$ is the $N$-copy state and $g,h\in S_N$ are permutations. The twist operator $\mathcal{T}_R(g)$ permutes the $N$ replicas within region $R$ according to $g$. For pairs $(g,h)$ satisfying the spherical condition, we show that the phase of the correlator is determined by the chiral central charge $\mathfrak{c}_{-}$ through $Z_{g,h}/\left\lvert Z_{g,h}\right\rvert=(\theta_g\theta_h/\theta_{gh})^{\mathfrak{c}_{-}}$, where $\theta_g^{\mathfrak{c}_{-}}$ is the topological spin of the twist defect labeled by $g\in S_N$. The construction applies to both bosonic and fermionic systems. We derive the formula within a field-theoretic framework under suitable assumptions and further test it numerically in microscopic lattice models. Our results establish a universal connection between real-space entanglement structures and the chiral central charge, providing a systematic framework for characterizing chiral topological phases directly on the lattice.

Emergent generalized symmetries and the holographic principle play very important roles in understanding quantum phase transitions. In recent years, tensor-network renormalization with generalized symmetry and the corresponding fixed-point tensor formulation have been proposed as a discrete spacetime framework for reformulating conformal field theory. Nevertheless, a complete holographic formulation within this framework is still lacking, and the current formulation does not directly accommodate sector partition functions that are modular covariant in general. In this work, we formulate $\mathcal{R}$-TNR, which builds the categorical constraints of a fusion category $\mathcal{R}$ into local tensor spaces and preserves these constraints under Loop-TNR. For suitable choices of $\mathcal{R}$, the initial tensors constructed here flow under $\mathcal{R}$-Loop-TNR to stable gapless fixed points. In the Ising, tricritical Ising, and three-state Potts conformal field theory examples, a broad range of initial parameters leads to the same gapless fixed point in each example. The method resolves conformal towers by anyon sector and yields scaling dimensions, conformal spins, and magnitudes of sector-resolved structure constants with extremely high accuracy compared to previous methods. These results realize a topological bootstrap based on stable symmetry-topological-order in which finite categorical and geometric input, together with an initial tensor that need not be fine-tuned, suffices to recover the infrared conformal field theory and its sector-resolved conformal data.

In two-dimensional (2D) flat-band systems, as engineered, for instance, by stacking and twisting van der Waals materials, the momentum dependence of the Bloch states is a key factor in determining the interaction-induced emergence of different phases. Hence, methods of probing this form of ”quantum geometry” are crucial to understanding these systems. Yet, extracting the momentum dependence of the underlying quantum geometric tensor from measurements is challenging in 2D. Here, we propose employing a quantum twisting microscope (QTM) with a sublattice-polarized tip to fill this gap. We show how expectation values of sublattice Pauli matrices can be probed across the scanned momentum path. This allows for the direct measurement of crucial symmetries characterizing the different candidate instabilities in graphene-based moiré systems. We furthermore show that the quantum metric component along the scan direction can also be extracted; the full quantum geometric tensor is also accessible, given that more than one sublattice polarization can be used. Our work illustrates the potential and extends the versatility of the QTM approach. If implemented in future experiments, this would provide unprecedented access to the symmetry signatures of the correlated phases and to the underlying quantum geometry in twisted bilayer graphene and related systems.

The Mpemba effect challenges the intuition that states closer to equilibrium must relax faster. We ask whether an analogous magic-ordering reversal can occur in the generation of quantum magic (nonstabilizerness), a key resource for universal quantum computation: can a state with less initial magic overtake one with more and reach its asymptotic value sooner? Here, we uncover interaction-induced dephasing as a distinct mechanism for this magic Mpemba effect, requiring neither transport nor conventional thermalization. For tilted product states in an interacting $\ell$-bit model, a random-phase analysis predicts a reversal of the magic ordering: states with less initial magic attain higher saturated magic, independent of their spatial pattern. Exact simulations of the $\ell$-bit model and localized spin chains further show that these states also saturate earlier. We observe both features on IBM superconducting quantum processors. An effective $\ell$-bit implementation accesses long dephasing times at fixed circuit depth by encoding time in gate angles, while a microscopic spin model exhibits the reversal universally across initial patterns in the localized regime but only selectively in the ergodic regime. These results establish interaction-induced dephasing as a route to anomalous quantum-resource relaxation beyond transport-driven thermalizing dynamics.

The photon-drag effect is a nonlinear optical phenomenon in which the finite momentum carried by incident photons is transferred to charge carriers, thereby generating a dc photocurrent even in systems with inversion symmetry. Within the density-matrix formalism in the velocity gauge, and accounting for nonvertical optical transitions driven by finite photon momentum, we derive the nonlinear injection and shift conductivities that characterize the photon-drag photogalvanic response. We investigate these photon-drag responses in unconventional $p_x$-wave and $d_{x^2-y^2}$-wave magnets in the presence of Rashba spin-orbit coupling (RSOC), highlighting the distinct roles of symmetry and quantum geometry in shaping their nonlinear optical behavior. The key finding of our work is that, despite the broken inversion symmetry, the conventional photogalvanic response vanishes identically in the $q=0$ limit after Brillouin-zone integration in both unconventional magnetic phases, resulting in a nonlinear dc photocurrent entirely photon-drag driven. The two unconventional magnets exhibit qualitatively distinct responses governed by their symmetry properties: the $p$-wave magnet supports only linear injection and circular shift conductivities, whereas the $d$-wave altermagnet, which simultaneously breaks time-reversal and inversion symmetries, admits all linear and circular components. Our findings establish altermagnets as a promising platform for controlling symmetry-selective nonlinear photocurrents and may enable applications in polarization-sensitive photodetection, nonlinear optoelectronics, and quantum geometric photogalvanics.

Lead-free ferroelectric BaTiO3 (BTO) nanoparticles with stabilized tetragonal distortion were synthesized via a ligand-assisted sol-gel method to serve as the active piezoelectric phase in high-performance hybrid piezoelectric nanogenerators (PENGs) operating with triboelectric synergy. XRD, Raman spectroscopy, and Pair Distribution Function (PDF) analysis confirmed pseudo-cubic tetragonal BTO nanoparticle, annealed at 900{\deg}C (BTO-900, ~54nm) and well-defined tetragonal BTO annealed at 1200{\deg}C (BTO-1200, ~104nm). Density Functional Theory (DFT) calculations confirmed enhanced Ti-O covalency, stronger Ti 3d-O 2p hybridization, narrower HOMO-LUMO gap, and improved dipole coherence in BTO-900, indicating superior ferroelectric polarization, piezoelectric activity, and charge retention. BTO-900-PDMS PENG device generated a high open-circuit voltage of ~100 V and stored ~29 {\mu}J energy, and superior capacitor-charging performance of BTO-900, while the optimized BTO-1200 based device showed a higher power density of ~649 {\mu}W cm-2 and short-circuit current of ~181 {\mu}A. The superior performance of BTO-900 was attributed to enhanced defect-assisted charge trapping, interfacial polarization, and impedance-controlled charge retention. By coupling the intrinsic piezoelectric response of covalency-engineered tetragonal BTO with triboelectric charge generation at the BTO-PDMS interface, this work establishes nanoparticle size and bonding engineering as an effective route to high-output, lead-free piezoelectric nanogenerators for self-powered electronics.

Physical many-body quantum systems typically interact locally, giving rise to ground states where entanglement grows with the area of the region being probed. Beyond entanglement, non-stabilizerness (or "magic") has been established as another crucial resource linked to quantum complexity and the properties of error-correcting states. Unlike entanglement, non-stabilizerness typically behaves with a volume-law scaling in ground states, indicating inherent computational complexity. In this work, we show that under a recent classification of quantum states, area-law states split into two distinct classes. Entanglement-dominated states obey an area-law for non-stabilizerness and admit efficient quantum algorithms for entanglement manipulation. Conversely, magic-dominated states exhibit a a faster-than-area growth of subsystem non-stabilizerness and require non-efficient algorithms for entanglement manipulation tasks. Within this context, we introduce the concept of the stabilizer regime, a restricted quantum phase that admits efficient entanglement manipulation and hosts area laws for both magic and entanglement.

Uniaxial ferroelectrics have long served as benchmark systems for time-resolved studies of polarization evolution due to their simple 180-domain structure. However, recent experiments in these materials have revealed complex topological textures with enigmatic features, including the unexpected charge-free head-to-head and tail-to-tail domain walls which still wait for their consistent explanation. Here, we use a universal three-dimensional phase-field model to investigate the kinetics of domain structure development in triglycine sulfate, accounting for the monoclinic symmetry of its parent and ferroelectric phases. We show that isolated saddle-like polarization structures, interconnected saddle cascades, saddle lines and specific monkey saddles can form only when transverse degrees of freedom for spontaneous polarization are allowed in the polar plane of a uniaxial ferroelectric. The abundance and diversity of saddle-like structures at the early stages of domain ordering drives a far more effective compensation of bound charges at head-to-head and tail-to-tail domain walls than those predicted by single-component order parameter models. As domains coarsen and residual bound charges migrate toward the surfaces of the sample, the topological landscape simplifies, leaving behind only isolated saddle points. The present model successfully reproduces exotic structures observed experimentally in triglycine sulfate and lead germanate and reveals a domain topology that extends beyond the conventional Ising picture of uniaxial ferroelectrics. Although the mechanisms of bound-charge compensation are likely to be material-specific, similar topological structures may emerge in other uniaxial ferroelectrics. The general formulation of our phase-field model opens the way for future studies of such phenomena across a broader class of ferroelectric materials of arbitrary symmetry.

Broadly studied origami crease patterns such as the Miura-ori are capable of rigid folding that maintains their spatial periodicity. However, periodic crease patterns generically require additional creases and fold into quasi-cylindrical shapes. Here, using group theory, we show that the folding properties of such sheets are largely determined by their spatial symmetries, known as layer groups. Within each symmetry class, the allowed linear shape-periodic modes of sheets are constrained and classified by the irreducible representation they belong to. Such classification further gives a sufficient condition, containing a symmetry constraint and a topological constraint, for the existence of a nonlinear strain mode. In this way, familiar special cases are placed within a unified framework that connects symmetry, network topology, and deployability. Finally, we turn our classification results into a predictive design principle that enables the rapid design of novel sheets with prescribed properties.

Grain-boundary (GB) segregation in austenitic Fe-Cr-Ni alloys has been studied mainly in irradiated or sensitised material, rarely in the nanocrystalline state. Hybrid molecular dynamics/Monte Carlo (MD/MC) simulations are used to segregate three independent nanocrystalline Fe-18Cr-12Ni polycrystals, which are compared with annealed and random controls on the same microstructures. Ni is depleted at the GB plane and Cr is enriched in the adjacent atomic shell; both directions are established at the production sampling budget and strengthen when one of the three microstructures is sampled further. The Cr enrichment is resolved only against the far-field grain interior; the common partition into face-centred-cubic (fcc) and non-fcc atoms places the enriched shell in its own reference. Under a constant uniaxial stress of 4.6 GPa at 300 K, the segregated polycrystals take about 16% longer than random ones to reach 50% strain; measured against annealed controls, boundary chemistry contributes about two-thirds of this gain and boundary relaxation the rest. The difference arises from a lower strain rate early in plastic flow, with no resolvable change in dislocation content. At a fixed strain rate the segregated state has a 6-7% higher peak stress than its annealed control at 300, 750 and 950 K, and at matched ratios of applied to flow stress the gain is the same at all three temperatures, decreasing only as that ratio rises. Early plastic flow is thus the stage at which GB chemistry acts, and simulated GB composition in nanocrystals depends strongly on the reference region.

We consider a modular associative neural network made of $L$ Hopfield models (HMs), coupled so that intra-module interactions are Hebbian and inter-module interactions are anti-Hebbian; this competitive coupling is known to endow the network with pattern-disentanglement capabilities. The integral representation of this system coincides with an assembly of $L$ restricted Boltzmann machines (RBMs) whose hidden layers are coupled, thereby extending the HM-RBM duality to the modular setting. We then train this modular RBM, via one-step contrastive divergence, to perform a classification task in which a query encoded on the visible layers is mapped onto an $L$-tuple of labels read off the hidden layers. When the query is composed of $L$ patterns that are mutually orthogonal on average, we prove that the RBM weights obtained as empirical means over the training dataset, as suggested by the HM-RBM equivalence, constitute a fixed point of the learning dynamics, and we derive an explicit, non-asymptotic bound on the residual drift. We then turn to a harder classification task in which each module is queried with a mixture of $L$ patterns and we show numerically that the same setting for the RBM weights still provides an effective set-up, letting the network jointly classify and disentangle the mixture.

We study the $d$-dimensional generalization of Models II ($d=2$) and V ($d=3$) for liquid crystals introduced by Heilmann–Lieb (1979), which consists of dimers on the hypercubic lattice at chemical potential $\mu$, interacting via a hard-core repulsion and a lateral attraction between parallel dimers with coupling constant $b>0$. For $d\in\{2,3\}$, these models were conjectured to exhibit liquid-crystalline order at low temperatures provided that $\mu+2(d-1)b>0$. We establish nematic order for all $d\ge 2$ under the additional condition $(4d-6)b>\mu$, which corresponds to the physical regime in which misaligned dimers are rare on scales comparable to the correlation length of the one-dimensional reference system. While the treatment of orientational order here follows the approach of our recent work on Model I, the proof of the absence of translational order relies on a custom implementation of cluster swapping in the sense of Sheffield (2005). Consequently, we deduce uniqueness of Gibbs measure and anisotropic exponential decay of correlations within each oriented phase.

We discuss free-energy estimation for complex systems using simulated tempering with Wang–Landau-type feedback. We show that introducing nonreversible dynamics in temperature space and multiple temperature updates per step significantly accelerates the convergence of the free-energy estimate. We then apply the algorithm to the three-dimensional Edwards-Anderson spin-glass model. Our results show that the algorithm can precisely estimate the free energy up to a large system size $L \simeq 64$, and that subsequent equilibrium simulated tempering simulations with the estimated free energy can rapidly sample from the Boltzmann distributions over a wide temperature range that covers the spin-glass transition temperature. The convergence time of our algorithm grows much more slowly with system size than that of another known algorithm for on-the-fly free-energy estimation.

Local-basis Shannon entropies of critical wave functions contain universal subleading information, but the Shannon point of the critical transverse-field Ising chain is singular in the conventional Rényi approach. We treat it directly at $n=1$ by representing the complete computational-basis Born distribution as the odd-degree boundary of independent long-range Bernoulli edges. The Shannon chain rule separates the entropy into explicit independent-edge and conditional cycle-space terms. For the periodic chain this isolates the analytic edge anomaly and organizes the remaining constant by linked vertex support. Conditional on the stated finite-part matching and forest assumptions, every nonvanishing linked coefficient is represented by an explicit finite-dimensional integral, giving an all-orders analytic hierarchy; the four-vertex term is evaluated in closed form, and the first few linked sectors already nearly saturate the established periodic constant, which is also reconstructed independently from the exact finite-size distribution. For an interval, the exterior reduces exactly to one ghost vertex and the explicit squared logarithms cancel, leaving the analytic edge contribution $\gamma_E=\log2/4-1/16$. The conditional cycle term has an exact all-support decomposition into physical-line and ghost-linked sectors; conditional on closure of the boundary forest subtraction, these sectors define an all-orders hierarchy of renormalized line and monomer–dimer boundary periods for the remaining logarithmic coefficient. The first complete augmented linked coefficient is evaluated in closed form, with an exact cancellation between its line and ghost boundary-layer anomalies; an independent reconstruction from exact finite-size probabilities recovers the established coefficient $\gamma_1=0.060020(3)$.

We compute the temperature dependence of effective spin-model parameters in two-sublattice ferrimagnets with antiparallel and inequivalent sublattice magnetizations using Green's-function theory. The effective intra- and intersublattice exchange interactions, together with the sublattice anisotropies, exhibit distinct thermal renormalizations arising from the different magnetic interactions and correlations of the two sublattices. Although these effective interaction parameters decrease monotonically with increasing temperature, their unequal renormalization produces a strongly nonmonotonic and polarization-dependent long-wavelength spin-wave response. In particular, the spin-wave exchange stiffness exhibits a strongly branch-dependent and nonmonotonic temperature dependence. One polarization develops an enhanced spin-wave stiffness in the vicinity of the angular momentum compensation region despite the monotonic thermal reduction of the underlying exchange interactions. The Green's-function predictions are in quantitative agreement with atomistic spin-dynamics simulations, which provide a numerical benchmark including thermally induced spin correlations within the underlying atomistic spin model. These results establish a direct connection between temperature-dependent atomistic interactions, long-wavelength spin-wave stiffness, and the effective parameters required for finite-temperature micromagnetic and multiscale modeling of ferrimagnetic materials.

We propose a finite-temperature Gaussian-fluctuation formalism for response functions within ghost rotationally invariant slave-boson (gRISB) theory and apply it to the two-dimensional Hubbard model. The gRISB magnetic phase boundary and static spin and charge susceptibilities capture the trends of dynamical mean-field theory (DMFT), significantly improving upon standard RISB and the random phase approximation (RPA). At the RISB level, our formalism recovers the Kotliar-Ruckenstein response. The dynamical susceptibilities resolve paramagnons, low-energy sound modes, and high-energy Hubbard excitations. Because they are evaluated directly on the real-frequency axis, the results avoid Matsubara truncation, stochastic sampling, and numerical analytic continuation. We also introduce a conserving quasiparticle approximation that expresses the response in terms of dressed Green's functions and vertex corrections.

An Andreev spin qubit stores a single unpaired spin, yet its coupling to the superconducting phase can be dominated by coherent virtual quasiparticle pairs. We develop a continuum variational description of the odd-parity doublet in a quantum-dot Josephson junction with Coulomb interaction and spin-dependent background tunneling. Retaining configurations with up to two Bogoliubov quasiparticles provides compact analytical expressions for energies and wavefunctions. We benchmark the results against numerical renormalization group calculations and identify sources of error. We obtain closed-form expressions for the conventional and spin-dependent Josephson couplings. Despite their small probability, two-quasiparticle configurations, through coherence with the zero-quasiparticle component, supply exactly half of the leading spin-dependent Josephson coupling even without Coulomb repulsion and dominate it as the repulsion grows. Spin-orbit-induced spin transfer between the dot and the leads produces a Josephson-current contribution that is common to both qubit states and finite at zero phase bias when the dot and lead Zeeman energies differ. We also map the localization of the virtual quasiparticles and the spin density in the leads. The results connect strongly correlated quantum-dot models to effective Hamiltonians used for Andreev-spin-qubit circuits and clarify how the wavefunction structure determines their couplings.

Conductive metal-organic frameworks (c-MOFs) are promising electronic materials, where electronic states critically determine electrical conductivity. However, achieving controllable modulation of these states during crystallization remains challenging. Existing approaches rely either on redesigning framework components or on introducing external dopants after crystallization, making electronic-state regulation dependent on structural modification or postsynthetic doping. Here, we demonstrate a crystallization-enabled in situ proton-management strategy for regulating the electronic state of c-MOFs. Using Co9HHTP4 as a model system, we show that distinct proton environments influence the balance between competing proton-coupled electron-transfer pathways during Co-O framework assembly while preserving the fundamental framework architecture. HNO3-mediated crystallization produces an electronic state consistent with enhanced electron retention within the Co-O framework and results in a single-crystal conductivity of 8.4 * 10-2 S cm-1, nearly four orders of magnitude higher than Co9HHTP4-NaOAc (1.7 * 10-5 S cm-1), together with a substantially reduced transport activation energy. Hall measurements further reveal a pronounced increase in carrier concentration for Co9HHTP4-HNO3, providing direct evidence that the enhanced conductivity is associated with a substantially increased carrier population. These results establish crystallization conditions as an active parameter for programming electronic states and charge transport in conductive frameworks.

In colloids, anisotropy in either shape or particle interactions can steer assemblies away from close-packed monolayers and towards more intricate structures. In this study we utilize both shape and interaction anisotropy to stabilize porous surface assemblies of triblock elliptical particles, whose surfaces are decorated with two attractive patches at opposite poles. The resulting structures display a tunable degree of crystalline kagome order, controlled by quenching the temperature and/or changing the chemical potential. In particular, we find evidence that nucleation into the kagome lattice proceeds via a one-step pathway, in contrast to the two-step route widely reported in spherical triblock systems, making triblock ellipses an interesting model system for studying how self-assembly pathways change with particle shape. Beyond ordered crystalline structures, we find disordered porous networks with complex internal geometry. To characterize this range of assemblies, we introduce a particle-patch graph that explicitly captures the localization of bonds at distinct patches. Bonding motifs follow directly from this representation, while the loops, that we identify as the pore boundaries, can be determined from the graph's planar embedding. We detect all loops as the face boundaries in the planar embedding by means of a face-walking algorithm, distinct from shortest-path approaches used in ring detection. Together with a new local and global order parameter measuring the loop network's regularity with respect to a selected loop size, this framework connects microscopic bonding motifs to mesoscopic pore properties and quantifies the tunable order of these porous assemblies.

We extend the dynamical vertex approximation (D$\Gamma$A), in its most commonly used ladder-version, to systems with retarded electronic interactions. Such an extended scheme, which we name "dynamical-$U$ D$\Gamma$A", allows us to study strongly interacting electrons coupled to bosons including non-local spatial correlations on all length scales on top of the purely local ones captured by dynamical mean-field theory. We demonstrate the applicability of the method in the specific case of the coupling to a single dispersionless phononic mode, by studying the Hubbard-Holstein model on the square and cubic lattices, focusing on regimes of sizable Hubbard interactions where strong electronic correlations compete with phonon-mediated interactions. As illustrative examples, we consider the antiferromagnetic phase in the three-dimensional model and the d-wave superconductor in two dimensions, analyzing the effect of the electron-phonon coupling, including its frequency dependence, on both instabilities.

Based on the analysis of moiré superlattice characteristics and interlayer hybridisation in small-angle twisted graphene multilayers with a monolayer hexagonal boron nitride (hBN) spacer, we predict spectral features and quantum transport effects in these systems. Here, we consider both a twisted bilayer and double bilayers with a spacer, discuss double bilayers in two stacking orders - with and without inversion symmetry - and also compare the results obtained with self-consistent Hartree calculations with and without in-plane periodic charge distribution, offering computationally efficient models for these graphene/hBN/graphene moiré systems. We note parametric intervals where the appearance of minibands can be enhanced by tuning with an out-of-plane displacement field, and identify the miniband edges and van Hove singularities across a broad range of densities and displacement fields. These system host Lifshitz transitions at which the Fermi lines form a network across moiré Brillouin zones, and to which Brown-Zak oscillations converge at low magnetic field and elevated temperatures. We analyse interlayer hybridisation across the same parameter space, discuss how hybridisation affects in-plane magneto-transport in ultra-high-mobility structures, and predict that semiclassical magneto-oscillations of interlayer hybridisation can lead to 1/B-periodic quantum oscillations of resistivity persistent to high temperature.

We study how independently trained Transformer neural networks reconstruct a binary string from its local domain walls. Runs sharing the data and training protocol can realize different functions. We treat them as replicas and measure truth alignment $m$, prediction confidence $q_{\mathrm{self}}$, and cross-replica agreement $q_{\mathrm{cross}}$. Confident disagreement defines the finite-size replica fragmentation that we call glass-like. With small training sets, replicas predict all training examples correctly but remain confident in incorrect predictions for unseen inputs, a regime we call memorization. With larger sets, runs can generalize and then retreat. Retreat occurs when outputs start to deviate from truth while confidence remains high. The frontier between learned and unlearned outputs recedes toward shorter strings. Many later recover as the frontier advances again. The self–cross gap $q_{\mathrm{self}}-q_{\mathrm{cross}}$ clearly distinguishes the three learning regimes of memorization, retreat, and recovery. With overall and position-dependent truth alignment subtracted, their residual correlations also differ: memorizing replicas have weakly and uniformly correlated residuals, while retreat has the largest fraction of replica pairs whose residuals are anti-correlated. That is, on the inputs where one replica of such a pair does better than its average, the other tends to do worse. These finite-size observations distinguish persistent memorization from ongoing retreat–recovery dynamics. The thermodynamic and long-time limits, and extensions to other learning tasks, remain open.

Engineering magnetism in two-dimensional semiconductors through interfacial interactions offers an attractive alternative to substitutional doping and provides opportunities for integrating magnetic and optoelectronic functionality within the same heterostructure. Here, we investigate ultrathin VOx films deposited on monolayer MoSe2 and demonstrate a pronounced enhancement of the magnetic response upon formation of the VOx/MoSe2 interface. Combined structural, spectroscopic, magnetic, and first-principles analyses support a consistent picture in which finite VOx clusters possess intrinsic magnetic moments that are further enhanced by electron transfer from MoSe2 to the oxide. The predicted charge transfer is also consistent with the increased trion contribution observed in the photoluminescence response of the heterostructure. Beyond this interfacial enhancement, the magnetic behavior is strongly governed by the morphology of the ultrathin oxide. A crossover from discontinuous clusters to more continuous films produces qualitatively different temperature dependences: the continuous-film regime exhibits conventional thermal demagnetization and coercive softening, whereas the clustered regime displays an unusual increase in magnetization and nonmonotonic coercivity with increasing temperature. These contrasting responses are captured by a phenomenological model in which morphology determines the collective magnetic dynamics through a distribution of effective reversal barriers and their thermally activated accessibility. Together, the results establish a unified picture in which interfacial charge transfer enhances the local magnetic moments of VOx, while nanoscale morphology governs their collective magnetic dynamics, providing complementary routes for controlling magnetism in oxide/transition-metal dichalcogenide heterostructures.

We investigate the statistical mechanics of a system coupled to multiple heat reservoirs at different temperatures, a setting which typically sustains nontrivial circulation. By applying a canonical transformation, we map the system onto that of a particle coupled to a single reservoir yet driven by a deterministic curl-force—a reversible, velocity-independent non-conservative force with non-vanishing curl—that can be described by a Hamiltonian with an anisotropic kinetic energy term. Despite the Hamiltonian structure, the system does not relax to the corresponding Boltzmann distribution, and is genuinely out of equilibrium. The mapping provides a mechanical interpretation of the currents in multi-temperature systems, as we demonstrate by means of two examples. In particular, the direction of circulation is qualitatively predictable from the deterministic force field. For the exactly solvable case of an $N$-dimensional underdamped Ornstein-Uhlenbeck process, we derive explicit expressions for the steady-state distribution and the entropy production rate, highlighting the role of the (generalized) curl of the force field in driving the system out of thermal equilibrium. Finally, we show how a non-conservative force can be used to exactly equilibrate any system coupled to multiple reservoirs, and obtain the corresponding equilibrium distribution.

In this report we analyze charasteristics of structural symmetry of small AkBlCm nanoclusters (A - Rb, Cs; B - Pb, Sn, Bi; C - Cl, Br, I), binding energies, stability, and, ultimately, applicability as building blocks for construction of larger-size nanoclusters. Preliminary spatial modeling of ternary compound nanoclusters has been carried out on the basics of geometrical approach, namely interatomic distances taken as a sums of corresponding ionic radii. The geometry optimization and binding energies of the modeled structures have been determined through quantum-chemical calculations. Geometry optimization has been performed with Gaussian09 software package using Density Functional Theory (DFT) within the generalized gradient approximation of the Perdew-Burke-Ernzerhof (PBE) and hybrid approximation of the Becke-3-Lee-Yang-Parr (B3LYP) exchange-correlation functionals. The Stuttgart/Dresden (SDD) and Los Alamos National Laboratory 2 Double Zeta (LANL2DZ) scalar-relativistic effective basic potentials were employed throughout the calculations. As a result of these calculations, a clear relationship between the atomic radii, their ratios within the nanoclusters and their stability has been obtained and analyzed.

Waterfall-like spectral features observed by angle-resolved photoemission spectroscopy (ARPES) are commonly associated with strong electronic correlations or electron-boson coupling. Here, we investigate this connection in the kagome metal LuFe6Ge6, a structurally simple member of the FeGe-derived family, using polarization-dependent ARPES, density functional theory and dynamical mean-field theory. We observe a pronounced vertical spectral feature at the L point extending over several hundred meV in binding energy. Its orbital character is identified as predominantly Fe dyz, and its energy onset coincides with a van Hove singularity located approximately 0.3 eV below EF . Despite the waterfall-like spectral response, dynamical mean-field theory (DMFT) reveals only weak electronic correlations, while the calculated electronic structure closely reproduces the experimental bulk bands. We propose that the anomalous spectral weight may arise from inelastic scattering of the outgoing photoelectrons, potentially associated with the large density of states near the van Hove singularity. Our results suggest that waterfall-like features can emerge without strong electronic correlations and highlight the possible role of the underlying band structure and photoelectron energy-loss processes in their interpretation.

Beyond the frozen-pairing contribution, the superfluid weight of a multiband superconductor contains a correction from the self-consistent relaxation of the pairing amplitudes under a phase twist. We show that this correction has a quantum-geometric origin, not in the space of Bloch states but in the space of collective pairing fields. For an attractive multiband Hubbard model at the mean-field level, the thermodynamic Hessian governing the pairing response coincides with the static Gaussian pair-fluctuation kernel at zero momentum at every temperature below $T_c$. Since gauge invariance relates a phase twist to a finite center-of-mass momentum of the pair field, the superfluid weight is set by the small-momentum curvature of the eigenvalue branch that evolves from the Goldstone mode, and the relaxation correction is a stiffness-weighted quantum metric of the corresponding soft eigenvector on the manifold of pairing configurations. The same construction yields the Ginzburg-Landau gradient coefficient with the identical geometric correction, hence the coherence-length tensor, and, with the low-frequency dynamics of the kernel, the pair-mass tensor. Lieb-lattice calculations verify the equivalence of the thermodynamic, fluctuation-kernel, and soft-mode formulations and the independence of the superfluid weight from the orbital embedding.

We compute analytically the leading beyond-ring corrections to the static irreducible polarizability of the two-dimensional (2D) electron gas, namely the two exchange self-energy diagrams and the exchange vertex diagram, each of first order in the Coulomb coupling, and insert the resulting polarizability into the RPA geometric series to obtain the static dielectric function and screened interaction. The self-energy and vertex contributions individually diverge; we obtain both divergent pieces in closed form. Their sum is finite and reproduces exactly the Hartree-Fock compressibility, which renormalizes the Thomas-Fermi wave vector. We show that exchange converts the one-sided 2D Kohn kink at 2k_F into a sharp two-sided peak, a qualitative improvement over Thomas-Fermi and RPA screening. In real space this makes the Friedel oscillations around a charged impurity 2-3 times larger than in RPA, with an amplitude that increases with distance over the range studied; implications for Kohn-Luttinger pairing are discussed. Relation to earlier works on the same diagrams is discussed.

We study the interplay between symmetry defects insertion and the phenomena of quantum many body scarring. We exploit a class of models obtained from an embedding mechanism that defines a stochastic matrix form hamiltonian, hosting zero energy many body scarred states. Such models display an interesting playground to explore the consequences of dualities, half-gauging operations and so on. We first show that inside this class of models, what are the conditions to still have scared states after defect insertion. The main result of our work is a detailed analysis of half-gauging in such chains, which introduces a non-trivial interface in our system, leading to scarred states protected by the underlying symmetries. The conclusions for half-gauged scarred systems are general and may lead to fruitful directions for higher dimension scarred physics and their robustness.

Physical crosslinks in conventional gels are static and spatially localised, fundamentally limiting their capacity to adapt, self-heal, or perform mechanical work. Topological gels, which are held together by physical entanglements such as threadings, links, and mechanical interlocks, constitute a different paradigm by treating connectivity as a mobile, dynamic degree of freedom. Here, by using molecular dynamics simulations of semiflexible polymers and threadable colloidal rings, we establish some general design principles that transform self-assembled topological gels into programmable soft materials. We present three different modes of control. First, by controlling the mobility of the entanglements, one can tune the mechanical response of the material. Quenched anchoring forces the network to store elastic stress and yield, whereas with annealed anchoring the material can relax stresses by redistributing its entanglements whilst preserving global connectivity. Second, by controlling the degree or type of geometric confinement, it is possible to template macroscopic architecture, converting for instance 3D isotropic gels into surface-spanning 2D nets or quasi-1D topological rings with distinct graph-spectral signatures. Third, by allowing dynamical rewiring of entanglements through polymer reconnection, the material topology can be rewritten after assembly, yielding interlocked structures dominated by simple pairwise links rather than the highly complex linked states previously observed in reconnecting flexible polymers. By establishing a direct link between microscopic entanglement dynamics and emerging mechanical function, our work offers design principles for adaptive soft metamaterials and provides insights into biological topological networks such as kinetoplast DNA and chromatin loop networks.