Papers

Neutral-atom quantum simulators provide a powerful platform for realizing strongly correlated phases, enabling access to dynamical signatures of quasiparticles and symmetry breaking processes. Motivated by recent observations of quantum phases in flux-frustrated ladders with non-vanishing ground state currents, we investigate interacting bosons on the dimerized BBH lattice in two dimensions-originally introduced in the context of higher-order topology. After mapping out the phase diagram, which includes vortex superfluid (V-SF), vortex Mott insulator (V-MI), and featureless Mott insulator (MI) phases, we focus on the integer filling case. There, the MI/V-SF transition simultaneously breaks the $\mathbb Z_2^{T}$ and U(1) symmetries, where $\mathbb Z_2^{T}$ corresponds to time-reversal symmetry (TRS). Using a slave-boson description, we resolve the excitation spectrum across the transition and uncover a chiral Higgs mode whose mass softens at criticality, providing a dynamical hallmark of emergent chirality that manifests via the oscillation of the loop currents in quench dynamics. Our results establish an experimentally realistic setting for probing unconventional TRS-broken phases and quasiparticles with intrinsic chirality in strongly interacting quantum matter.

Time-periodic modulation of a static system is a powerful method for realizing robust unidirectional topological states. So far, all such realizations have been based on interactions among $s$ orbitals, without incorporating inter-orbital couplings. Here, we demonstrate higher-orbital Floquet topological insulators by introducing periodically modulated couplings between the optical $s$ and $p$ orbitals in a square lattice. The staggered phase of the $s$-$p$ couplings gives rise to a synthetic uniform $\pi$ magnetic flux per plaquette of the lattice, and periodic driving of the couplings opens a topological bandgap, characterized by the Floquet winding number. We image topological edge modes of $s$-$p$ orbitals traveling unidirectionally around a corner. Here, the topological phases are realized by a combined effect of the periodic driving and synthetic magnetic flux. Consequently, when the synthetic flux is turned off, the system becomes trivial over a range of driving parameters. Our results open a promising pathway for exploring topological phenomena by introducing the orbital degree of freedom.

We consider a quantum mechanical model involving interacting fermions without disorder that has the same low energy physics as the supersymmetric SYK model. The model is $SU(2)$ invariant, and the supercharge involves the $ SU(2) $ 3j symbol. We analyze various solvable corners, conceptually explain why it has a melonic expansion, and perform an exact diagonalization for small values of $N$. Expanded around the states with maximal angular momentum, the model is approximated by a two dimensional CFT. The BPS states have a simple description in that regime.

Optical spectroscopy based on second-order nonlinearity is a critical technique for characterizing two-dimensional (2D) crystals as well as bioimaging and quantum optics. It is generally believed that second-harmonic generation (SHG) in centrosymmetric crystals, such as graphene and other bilayer 2D crystals, is negligible without externally breaking the inversion symmetry. Here, we show that with a new homodyne detection technique, we can apparently circumvent this symmetry-imposed constraint and observe robust SHG in pristine centrosymmetric crystals, without any symmetry-breaking field. With its exceptional sensitivity, we resolve polarization-resolved SHG in bilayer hexagonal boron nitride (h-BN), bilayer 2H-WSe$_2$, and remarkably, Bernal-stacked bilayer graphene, allowing us to unambiguously identify the crystallographic orientation in these crystals via SHG for the first time. We also demonstrate that the new technique can be used to non-invasively detect uniaxial strain and optical geometric phase in these crystals. The observed SHG in our experiments is attributed to second-order nonlinearity in the quadrupole channel, which is controlled by the presence of the $C_2$ symmetry instead of the inversion symmetry. Our new technique expands the capability of nonlinear optical spectroscopy to encompass a large class of centrosymmetric materials that could never be measured before, and can be used for quantum sensing of moiré materials and twisted epitaxial films.

At scales larger than the forcing scale, some out-of-equilibrium turbulent systems (such as hydrodynamic turbulence, wave turbulence, and nonlinear optics) exhibit a state of statistical equilibrium where energy is equipartitioned among large-scale modes, in line with the Rayleigh-Jeans spectrum. Key open questions now pertain to either the emergence, decay, collapse, or other nonstationary evolutions from this state. Here, we experimentally investigate the free decay of large-scale hydroelastic turbulent waves, initially in a regime of statistical equilibrium. Using space- and time-resolved measurements, we show that the total energy of these large-scale tensional waves decays as a power law in time. We derive an energy decay law from the theoretical initial equilibrium spectrum and the linear viscous damping, as no net energy flux is carried. Our prediction then shows a good agreement with experimental data over nearly two decades in time, for various initial effective temperatures of the statistical equilibrium state. We further identify the dissipation mechanism and confirm it experimentally. Our approach could be applied to other decaying turbulence systems, with the large scales initially in statistical equilibrium.

Even-denominator fractional quantum Hall (FQH) states can be viewed as topological superconductors of composite fermions, supporting a charged chiral mode and $|\mathcal{C}_{cf}|$ neutral Majorana modes set by the Chern number $\mathcal{C}_{cf}$. Despite ongoing efforts, distinguishing the many competing paired phases remains an open problem. In this work, we propose a unified theory of charge transport across a quantum point contact (QPC) for general paired FQH states described by an $so(N)_1 \times u(1)$ conformal field theory. We derive the boundary effective action for an arbitrary number of Majorana fermions $N=|\mathcal{C}_{cf}|$ and develop a non-perturbative instanton approximation to describe tunneling processes. We establish a weak-strong duality relating strong quasiparticle tunneling to weak electron tunneling. We calculate the scaling dimensions of the tunneling operators and demonstrate that while the weak-coupling fixed point is generally unstable, the strong-coupling fixed point is stable for physically relevant filling fractions and number of Majorana fermions. These transport exponents provide a distinct experimental fingerprint to identify the topological phases of even-denominator FQH states.

Biased sampling in molecular dynamics simulations overcomes timescale limitations and delivers free-energy landscapes, essential to understand complex atomistic phenomena. However, when applied across diverse systems and processes, biasing protocols often require time- and resource-consuming fine-tuning. In search for robustness, we boost a prominent biasing method, Umbrella Sampling. To estimate the value of an integral, i.e., the free energy, our Bayesian Umbrella Quadrature (BUQ) method iteratively selects gradient samples, i.e., bias locations, that most reduce the posterior integral variance based on a noise-tolerant Gaussian process model, which also effectively interpolates between samples. We validate the method for a conformational change in a small peptide, a water-to-ice phase transition, and a substitution chemical reaction; obtaining excellent accuracies and speedups. To ease adoption of this more automated and universal free-energy method, we interface BUQ with wide-spread simulation packages and share hyperparametrization guidelines.

Magnetic phases are commonly identified through macroscopic magnetization, yet many ordered states, including antiferromagnets and altermagnets, possess a vanishing net moment despite distinct local spin structure. We show that such an order can be accessed through the measurement-induced steady state of a single primary qubit locally coupled to a spin lattice. Using a controlled primary-ancillary qubit protocol, we derive analytically that the steady state encodes a locally weighted exchange field in a signed observable that is linear in the weak-coupling regime. Numerical simulations demonstrate lattice-scale resolution of antiferromagnetic and altermagnetic textures and robustness against short-correlated noise. Our results establish measurement-induced dissipation as a resource for detecting magnetic order through microscopic structure rather than through global moments.

We present a first-principles framework for the calculation of phonons in nanostructures with cyclic and/or helical symmetry. In particular, we derive a cyclic- and helical-symmetry-adapted representation of the dynamical matrix at arbitrary phonon wavevectors within a variationally formulated, symmetry-adapted density functional perturbation theory framework. In so doing, we also derive the acoustic sum rules for cylindrical geometries, which include a rigid-body rotational mode in addition to the three translational modes. We implement the cyclic- and helical-symmetry-adapted formalism within a high-order finite-difference discretization. Using carbon nanotubes as representative systems, we demonstrate the accuracy of the framework through excellent agreement with periodic plane-wave results. We further apply the framework to compute the Young's and shear moduli of carbon nanotubes, as well as the scaling laws governing the dependence of ring and radial breathing mode phonon frequencies on nanotube diameter. The elastic moduli are found to be in agreement with previous density functional theory and experimental results, while the phonon scaling laws show qualitative agreement with previous atomistic simulations.

The canonical model of stochastic search tracks a randomly diffusing "searcher" until it finds a "target." Owing to its many applications across science and engineering, this perennially popular problem has been thoroughly investigated in a variety of models. However, aside from some exactly solvable one-dimensional examples, very little is known if the searcher diffusivity varies in space. For such space-dependent or "heterogeneous" diffusion, one must specify the interpretation of the multiplicative noise, which is termed the Itô-Stratonovich dilemma. In this paper, we investigate how stochastic search with space-dependent diffusivity depends on this interpretation. We obtain general formulas for the probability distribution and all the moments of the stochastic search time and the so-called splitting probabilities assuming that the targets are small or weakly reactive. These asymptotic results are valid for general space-dependent diffusivities in general domains in any space dimension with targets of general shape which may be in the interior or on the boundary of the domain. We illustrate our theory with stochastic simulations. Our analysis predicts that stochastic search can depend strongly and counterintuitively on the multiplicative noise interpretation.

Spin transfer torques (STTs) control magnetisation by electric currents, enabling a range of nano-scale spintronic applications. They can destabilise the equilibrium magnetisation state by counteracting magnetic relaxation. Here, we maximise the STT effect through a dedicated growth-annealing protocol for CoFeB thin films, such that magnetic anisotropies originating from the interface and shape almost cancel each other. The nearly isotropic magnets enable low-current dynamical stabilisation of the magnetisation in the direction opposite to an applied magnetic field, thereby realising a spintronic analogue of the Kapitza pendulum. In an intermediate current regime, the STT drives large magnetisation vector fluctuations that cover the entire Bloch sphere. The continuous variable associated with the stochastic magnetisation direction may serve as a resource for probabilistic computing and neuromorphic hardware. Our results establish isotropic magnets as a platform to study as-yet-uncharted, far-from-equilibrium spin dynamics including anti-magnonics, with promising implications for unconventional computing paradigms.

For antiferromagnets composed of spin five-half ions, the moments of these ions in the ordered antiferromagnetic state can be significantly smaller than 5 BM (i.e., 1.56 - 4.48 BM) if these ions form quantum fluctuating entities (QFEs), for example, quasi one-dimensional uniform antiferromagnetic chains or quasi zero-spin antiferromagnetic spin dimers. It is reasonable to suppose that the stronger the quantum fluctuation in such an antiferromagnet, the greater the reduction in its ordered moment would become, but this supposition has not yet been confirmed because quantifying the strength of quantum fluctuation is not a straightforward matter. Here we show that the local magnetic excitations involving the QFEs can be used to quantify the strength of quantum fluctuation by analyzing six antiferromagnets showing significant reduction in their ordered spin moments.

Quantum devices require coherent coupling over macroscopic distances. Recently, resonances due to Klein tunneling and Andreev reflection states (KARS) have been observed in a naturally occurring p-n junction at the interface between Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ (BSCCO), a high-Tc superconductor (HTS), and graphene. The resonances appear as conductance oscillations with gating. Here, we show coupling between the KARS in BSCCO-graphene-BSCCO devices of varying separation (L). The coupling is evidenced by a power-law decay of resonance period as L increases from tens of nanometers to single microns. These results demonstrate the long-distance coupling of KARS cavities in graphene-HTS junctions. The length dependence seen in experiments is supported by single-particle spectral functions which show KARS are coupled by transport modes in graphene. The strong coupling between KARS in BSCCO-graphene-BSCCO junctions showcases the novelty of HTS-graphene junctions for quantum circuits and unconventional Josephson junctions.

We construct a $G$-cluster Hamiltonian in 2+1 dimensions and analyze its properties. This model exhibits a $G\times2\mathrm{Rep}(G)$ symmetry, where the $2\mathrm{Rep}(G)$ sector realizes a non-invertible symmetry obtained by condensing appropriate algebra objects in $\mathrm{Rep}(G)$. Using the symmetry interpolation method, we construct $S^1$- and $S^2$-parameterized families of short-range-entangled (SRE) states by interpolating an either invertible $0$-form or $1$-form symmetry contained in $G\times2\mathrm{Rep}(G)$. Applying an adiabatic evolution argument to this family, we analyze the pumped interface mode generated by this adiabatic process. We then explicitly construct the symmetry operator acting on the interface and show that the interface mode carries a nontrivial charge under this symmetry, thereby demonstrating the nontriviality of the parameterized family.

We construct 2+1-dimensional lattice models of symmetry-protected topological (SPT) phases with non-invertible symmetries and investigate their properties using tensor networks. These models, which we refer to as generalized cluster models, are constructed by gauging a subgroup symmetry $H \subset G$ in models with a finite group 0-form symmetry $G$. By construction, these models have a non-invertible symmetry described by the group-theoretical fusion 2-category $\mathcal{C}(G; H)$. After identifying the tensor network representations of the symmetry operators, we study the symmetry acting on the interface between two generalized cluster states. In particular, we will see that the symmetry at the interface is described by a multifusion category known as the strip 2-algebra. By studying possible interface modes allowed by this symmetry, we show that the interface between generalized cluster states in different SPT phases must be degenerate. This result generalizes the ordinary bulk-boundary correspondence. Furthermore, we construct parameterized families of generalized cluster states and study the topological charge pumping phenomena, known as the generalized Thouless pump. We exemplify our construction with several concrete cases, and compare them with known phases, such as SPT phases with $2\mathrm{Rep}((\mathbb{Z}_{2}^{[1]}\times\mathbb{Z}_{2}^{[1]})\rtimes\mathbb{Z}_{2}^{[0]})$ symmetry.

Double-helix (DH) nanowires provide a platform to study the influence of geometric chirality on spin chirality. Their three-dimensional (3D) helical architecture and tunable inter-strand coupling enable control of spin chirality, including the stabilization of topological 3D magnetic states such as helical domains and domain walls, topological stray fields, and extended helical vortex/skyrmion tubes. So far, the study of these and other 3D nanostructures is usually confined to a limited number of magnetic microscopy experiments in large facilities. Here, we investigate the reversal mechanism of a single DH nanowire using Dark-Field magneto-optical Kerr effect (DF-MOKE) magnetometry under external 3D magnetic fields. By analyzing the angular dependence of the DF-MOKE signal, we fit the reversal process using established models for domain-wall nucleation and propagation, finding a characteristic behavior similar to that reported for cylindrical nanowires. Micromagnetic simulations indicate that the reversal process goes through nucleation of the helical vortex tube in a curling manner while ptychographic X-ray magnetic circular dichroism data reveal that this helical vortex tube state forms through a mixed nucleation-propagation process. These observations provide a consistent microscopic picture of reversal mediated by a helical vortex tube extending along the nanowire. Our work provides a comprehensive characterization of magnetization reversal in DH nanowires and demonstrates that DF-MOKE magnetometry is effective for probing reversal mechanisms in single 3D nanostructures. This lab-based approach expands the range of accessible experiments beyond large-scale facilities, enabling extensive exploration of the rich spin states supported by 3D nano-geometries.

We study an open quantum spin chain with non-reciprocal dissipation using a theoretical approach known as time-dependent generalized Gibbs ensemble. In the regime of weak dissipation the system is fully characterized by its rapidity distribution and we derive a closed set of coupled differential equations governing their time evolution. We check the accuracy of this theory by benchmarking the results against numerical simulations. Using this framework we are able to compute both the magnetization density and current dynamics, identifying some relations between the two. The problem of the anomalous power-law exponents identified in a previous work is discussed. Our work constitutes a theoretical approach that is able to describe the physics of non-reciprocal open quantum spin chains beyond analyses based on non-interacting fermions.

This Ph.D. thesis reports on progress in rigorously establishing hydrodynamic principles from the microscopic Hamiltonian dynamics of quantum many-body systems in a general, non-model-specific manner. Using the C*-algebra framework of statistical mechanics, we treat systems directly in the thermodynamic limit, primarily focusing on quantum lattice models where tools such as Lieb-Robinson bounds yield rigorous statements. We thus provide a proof-of-principle that large-scale behaviours can indeed be seen as emerging from microscopic dynamics, with mathematical proof. We first report on ergodicity results in short-range models with exponentially decaying or finite-range interactions. We show that time-averaged observables converge to their ensemble averages and decorrelate from all other observables almost everywhere within the light-cone defined by Lieb-Robinson bounds. This relaxation property indicates the loss of information at large scales, from which we prove a Boltzmann-Gibbs principle: at the Euler scaling limit of large time and distance, observables project onto hydrodynamic modes (extensive conserved quantities), within correlation functions. These results hold independently of microscopic details, capturing the physical idea that such details are lost at large space-time scales. Regarding finer scales of hydrodynamics, we discuss rigorous lower bounds on the strength of diffusion. We establish a general result on the clustering of n-th order connected correlations within C* dynamical systems. These results are applied to obtain a strictly positive lower bound on the diffusion constant of chaotic open quantum spin chains with nearest-neighbor interactions. This thesis underlines the universality of hydrodynamic principles, provides a framework for establishing them rigorously, and sets the stage for future progress toward the goal of proving the hydrodynamic equations.

Periodic strain engineering in monolayer graphene provides a versatile platform to generate colossal pseudo-magnetic fields and flat pseudo-Landau levels directly in a single atomic sheet. While the electronic topology and transport properties of the normal state in these systems have been extensively studied, the superconducting ground state in such strain-modulated landscapes remains an unexplored frontier. In this work, we investigate the superconducting phase of periodically corrugated graphene using a self-consistent Bogoliubov-de Gennes framework. We find that, contrary to the conventional expectation that a high density of states universally enhances pairing, the macroscopic superconducting coherence is significantly hindered in the flat-band regions. This limitation originates from strain-induced sublattice polarization, where the zero-energy electronic states are spatially segregated between the $A$ and $B$ sublattices. Such spatial disjointedness hampers the inter-sublattice coherence required for a robust pairing instability, effectively decoupling the high-density flat-band states from the superconducting condensate. Consequently, as the pairing interaction increases, the system undergoes a striking spatial crossover: superconductivity sharply relocates from the flat-band regions to emerge as robust, quasi-one-dimensional filaments at the geometric nodes where local sublattice symmetry is restored. Our findings reveal that the spatial distribution of wavefunctions, governed by sublattice degrees of freedom, is a decisive factor in determining the superconducting properties of strain-engineered Dirac materials.

Excitons in monolayer transition-metal dichalcogenides (TMDs) have garnered significant attention because of their large binding energies due to weakly screened Coulomb interaction, and direct bandgap at the K/K$^\prime$ point in the hexagonal Brillouin zone featuring spin-polarised bands due to spin-orbit coupling and lack of inversion symmetry. This makes them prospective for next-generation optoelectronic and quantum devices. However, despite the intense research activity, the reported values for exciton binding energies, quasiparticle gaps, and spectral features exhibit substantial variation across both experimental and theoretical studies. In this article, we present a comprehensive and critical assessment of the current understanding of excitonic properties in single-layer TMDs, integrating results from the angle-resolved photoemission spectroscopy (ARPES), photoluminescence (PL) measurements, and other experimental techniques with first-principles theoretical insights. Special emphasis is placed on the comparison and reconciliation of discrepancies observed across different experimental setups and sample qualities. Furthermore, we highlight our state-of-the-art GW-BSE calculations, which include both equilibrium and laterally strained systems, to systematically analyse the behaviour of direct and indirect excitons. By evaluating the effect of strain as a tunable control variable, we demonstrate its potential to engineer excitonic properties, supported by cross-validation against prior theoretical predictions and experimental findings. In doing so, we clarify the sources of discrepancies in the literature and offer a unified perspective on excited-state engineering strategies in two-dimensional TMDs.

We present a finite-temperature canonical-ensemble determinant quantum Monte Carlo algorithm that enforces an exact fermion number and enables numerically stable simulations of correlated lattice fermions. We propose a stabilized QR update that reduces the computational complexity from standard cubic scaling $O(\beta N^3)$ to linear scaling $O(\beta N N_e^2)$ with respect to the system size $N$, where $N_e$ is the particle number. This yields a dramatic speedup in dilute regimes ($N_e \ll N$), opening unbiased access to large-scale simulations of strongly correlated low-density phases. We validate the method on the dilute Fermi gas with onsite Hubbard interactions, observing the suppression of the fermion sign problem in the dilute limit. Furthermore, we apply this approach to a one-dimensional flat-band system, where the canonical ensemble allows for precise control over filling. We reveal a ferromagnetic instability at low temperatures in the half-filling regime. Our linear-scaling approach provides a powerful tool for investigating emergent phenomena in dilute quantum matter.

The complexity of biomolecular interactions necessitates advanced methodologies to accurately capture their behavior in solution. In this work, we focus on monoclonal antibodies and adopt a multi-scale coarse-graining strategy for their modeling, with particular emphasis on the role of electrostatic interactions. Using scattering experiments, theoretical analysis, and large-scale computer simulations, we explicitly compare two selected case studies-markedly different in their charge distributions. Through mutually corroborating lines of evidence, we demonstrate that conventional approaches relying on electrostatic screening and implicit charge representations fail to capture the structural and thermodynamic properties of antibody solutions when strong charge heterogeneity is present, even at a moderate (amino acid) level of coarse-graining. These findings highlight the importance of a correct treatment of electrostatic interactions and ion screening for heterogeneously- and oppositely-charged colloidal and protein systems. Such considerations are essential to move beyond descriptive models towards a truly predictive framework, with direct implications for the formulation of therapeutics and the treatment of other complex soft-matter systems.

The paper reports on fundamental properties of the GaN/AlN quantum wells (QWs) with nominal subcritical thicknesses of 0.75-2 monolayers (MLs). They are grown by plasma-activated molecular beam epitaxy, varying either the nominal thickness or the gallium-to-nitrogen flux ratio. In situ monitoring reveals difference in 2D nucleation and step-flow growth modes of the QWs. The emission charactestics of QWs with integer thicknesses of 1 and 2 MLs depend weakly on the growth mechanism. In contrast, the intensity and spectral position luminescence of QWs with fractional-ML thicknesses are determined by the growth mechanism. Using ab initio calculations, a phenomenological model is proposed that describes fractional-ML QWs either as arrays of 2D quantum disks or as arrays of 2D quantum ribbons, in cases where 2D nucleation or step-flow growth mechanisms predominate, respectively. This model is generally consistent with experimental data on photo- and cathodoluminescence of heterostructures with multiple (250) GaN/AlN QWs. These heterostructures, when pumped by electrom beam at an energy 12.5 keV with a maximum pulse current of 2 A, exhibit linear current dependences of optical peak powers up to 1 and 37 W for wavelengths of 228 and 256 nm, respectively, making them promising for use as powerfull ultraviolet-C emitters.

Hour-glass clocks do not free-run; they keep time by riding an external rhythm. Motivated by the primordial KaiBC system in cyanobacteria, we study a driven, finite-state molecular clock that advances through a small number of biochemical states under an intrinsic driving energy and a rotating energy landscape set by day-night metabolism. In the continuum limit, coherence is maximized at a resonant operating point where the intrinsic drift matches the driving frequency. In realistic clocks with a finite number of states, discreteness matters: as the rotating landscape sweeps over a lattice of states, it generates a small and high frequency vibration of the collective phase that makes timing inaccurate. Combining the resonant cost with this discreteness penalty yields a trade-off in the number of states: few states are energetically cheap but noisy; many states are precise but costly. The optimum lies at moderate discretization (typically five to fifteen states) and an environmental coupling that is strong enough for responsiveness yet weak enough to avoid large discrete-state vibrations. These design rules rationalize why KaiC's hexameric architecture falls near the predicted optimum and suggest a general principle for hour-glass clocks across organisms.

When we consider canonical averages for classical discrete systems, typically referred to as substitutional alloys, the map phi from many-body interatomic interactions to thermodynamic equilibrium configurations generally exhibits complicated nonlinearity. This canonical nonlinearity is fundamentally rooted in deviations of the discrete configurational density of states (CDOS) from continuous Gaussian families, and has conventionally been characterized by the Kullback-Leibler (KL) divergence on discrete statistical manifold. Thus, the previous works inevitablly missed intrinsic nonlinearities induced by discretization of Gaussian families, which remains invisible within conventional information-geometric descriptions. In the present work, we identify and quantify such unavoidable canonical nonlinearity by employing the specific transport cost W'2on the 2-Wasserstein framework with a cost function aligned with the Fisher metric for Gaussian families. We derive an explicit expression for this transport cost W'2 in the limit of vanishing discretization scale d to 0. We further show that this limiting Wasserstein distance admits a clear geometric interpretation on the statistical manifold, equivalent to a KL divergence associated with the expected parallel translations of continuous Gaussian. Our framework thus provides a transport-information-geometric characterization of discretization-induced nonlinearity in classical discrete systems. In addition, we confirm that this W'2-KL equivalence admits a natural generalization beyond Gaussian families. The correspondence reveals that the irreversible geometric distortion of the local measure induced by discretization, while extrinsic to information geometry alone, can generically be characterized by a standard KL divergence.

The magnetic structure of EuTi$_2$Al$_{20}$, in which magnetic Eu$^{2+}$ ions form a diamond network, was investigated using neutron and resonant X-ray diffraction on powder and single-crystal samples. The propagation vector was determined to be $\textbf{\textit{q}}_{\rm m}=(1,0,0)$~r.l.u. from these diffraction measurements. All possible magnetic structures in the space group $Fd\bar{3}m$ with this propagation vector were examined using the irreducible representation method and magnetic space group analysis. This magnetic structure was identified as a collinear antiferromagnetic structure with the magnetic space group $P_Inna$ (\#52.320) or $P_Inn2$ (\#34.164) under zero magnetic field. In these magnetic structure, frustration arises from competing magnetic interactions on the diamond network. These findings provide a concrete experimental reference for assessing the role of competing interactions in diamond-network magnets and motivate further studies of interaction-driven quantum states.

It was conjectured for a long time that the tectonic plates are in a self-organised state of criticality and that the Gutenberg-Richter law is a manifestation of that. It was recently shown that for a system near criticality, the inequality of their responses due to external driving would sharply rise and show universal behavior that could indicate the proximity of the system to a critical point. As a result, measures such as the Gini and Kolkata indices that quantify inequality can also serve as indicators of imminent criticality and those of diverging (system-spanning) responses. In the context of earthquakes, such a large response would correspond to events of high magnitudes. In this work, we show with numerical simulations and seismic data analysis that large earthquake events have a tendency to follow events that are highly unequal, similar to the case of a system near a critical point. Even though this is not a proof of tectonic plate systems being near-critical, a continuous monitoring of the inequality indices of the earthquake time series could be an useful tool for hazard estimates. We have applied this framework to models of earthquakes as well as to the earthquake time series from various seismically active regions, such as North America, Southern Japan, parts of Southeast Asia and Indonesia. The findings indicate that the SOC picture of tectonic plates is consistent with the increase in size inequality of earthquakes, even though this cannot be treated as a rigorous proof.

The eigenstate thermalization hypothesis (ETH) posits how isolated quantum many-body systems thermalize, assuming that individual eigenstates at the same energy density have identical expectation values of local observables in the limit of large systems. While the ETH apparently holds across a wide range of interacting quantum systems, in this work we show that it requires generalization in the presence of thermal first-order phase transitions. We introduce a class of all-to-all spin models, featuring first-order thermal phase transitions that stem from two distinct mean-field solutions (two “branches”) that exchange dominance in the many-body density of states as the energy is varied. We argue that for energies in the vicinity of the thermal phase transition, eigenstate expectation values do not need to converge to the same thermal value. The system has a regime with coexistence of two classes of eigenstates corresponding to the two branches with distinct expectation values at the same energy density, and another regime with Schrodinger-cat-like eigenstates that are inter-branch superpositions; these two regimes are separated by an eigenstate phase transition. We support our results by semiclassical calculations and an exact diagonalization study of a microscopic spin model, and argue that the structure of eigenstates in the vicinity of thermal first-order phase transitions can be experimentally probed via non-equilibrium dynamics.

Defect engineering via parallel cracks has been proposed as a route to tailor the fracture response of graphene. However, atomistic fracture predictions can be strongly sensitive to the interatomic potential. Here, we quantify the effect of potential choice by revisiting H-passivated graphene containing two parallel cracks separated by a gap $W_{\text{gap}}$ loaded in tension along the armchair (AC) and zigzag (ZZ) directions. Molecular dynamics simulations using the AIREBO potential under the same geometry and loading protocol previously studied with ReaxFF, are employed, so enabling a direct comparison. Stress-strain responses, Young's modulus, an effective mode-I stress intensity factor, and energy absorption are evaluated as functions of $W_{\text{gap}}$. Compared with ReaxFF, AIREBO predicts lower peak stresses and earlier catastrophic softening, leading to reduced post-peak deformation capacity and energy absorption. Ductility and energy absorption are shown to be highly potential-dependent, underscoring the need for careful potential selection in defect-engineered graphene fracture simulations.

We study the spectral statistics and wave-function properties of a one-dimensional quantum system subject to a Cantor-type fractal potential. By analyzing the nearest-neighbor level spacings, inverse participation ratio (IPR), and the scaling behavior of the integrated density of states (IDS), we demonstrate how the self-similar geometry of the potential is imprinted on the quantum spectrum. The energy-resolved level spacings form a hierarchical, filamentary structure, in sharp contrast to those of periodic and random systems. The normalized level-spacing distribution exhibits a bimodal structure, reflecting the deterministic recurrence of spectral gaps. A multifractal analysis of eigenstates reveals critical behavior: the generalized fractal dimensions $D_q$ lie strictly between the limits of extended and localized states, exhibiting a distinct $q$-dependence. Consistently, the IPR indicates the coexistence of quasi-extended and localized features, characteristic of critical wave functions. The IDS shows anomalous power-law scaling at low energies, with an exponent close to the Hausdorff dimension of the underlying Cantor set, indicating that the geometric fractality governs the spectral dimensionality. At higher energies, this scaling crosses over to the semiclassical Weyl law. Our results establish a direct connection between deterministic fractal geometry, hierarchical spectral statistics, and quantum criticality.