arXiv subjects

Zohar Nussinov

Publications and source records attributed to Zohar Nussinov.

At least 19 recordsLinked to original sources

arXiv2026

Non-Maxwellian Velocity Statistics in Supercooled Liquids and Their Possible Relation to Super-Arrhenius Viscosity

For particles of fixed mass, classical equilibrium statistical mechanics dictates a Maxwellian velocity distribution determined solely by the temperature, regardless of the interactions, density, or structure. Supercooled glass forming liquids realize long lived metastable states that evade equilibrium crystallization and may thus violate assumptions underlying Maxwellian statistics. We numerically demonstrate that supercooled liquids can exhibit persistent non-Maxwellian velocity distributions with deviations connected to their exceptionally slow super-Arrhenius relaxation. Our work is motivated by a general result establishing that long lived metastable states may exhibit finite width distributions of intensive variables. A distribution of temperatures implies non-Maxwellian velocity statistics. We test this prediction by introducing stochastic thermostats that generate stationary states while, unlike conventional thermostats, not imposing Maxwellian velocity distributions. Simulations with these thermostats yield long lived states that have, by comparison to Maxwellian velocity distributions, an excess kurtosis $0<κ\lesssim0.3$. Crystallization is strongly impeded with increasing $κ$. In a minimal description, temperature fluctuations are characterized by a dimensionless width $\overline{A}$ with $κ\simeq3\overline{A}^{2}$. The nearly constant $\overline{A}$ (of an average value $0.08$ and standard deviation $0.03$) found in viscosity data collapse across $45$ glass formers and in specific heat signatures is consistent with kurtosis found in our simulations. Long time non-Maxwellian velocity statistics may thus link slow relaxation, transport, and thermodynamic measurements. Independent of the tested theory, the stochastic thermostats that we introduce offer a molecular dynamics route to non-Maxwellian velocity statistics.

cond-mat.stat-mech↗

arXiv2026

Giant nonlinear conductivity in 2D electron gas from substrate-induced dipolar scattering

Despite a surge of interest in the nonlinear transport in 2D materials, a fundamental puzzle remains: existing theoretical frameworks are unable to quantitatively account for the giant nonlinear conductivities ($\gtrsim 1 \frac{μ\text{m}}{Ω\text{V}}$) recently reported in 2D van der Waals heterostructures. Here, we introduce a mechanism based on electron scattering from a substrate-induced dipole array linked to short-range impurities. We show that the strict kinematic constraints, inherent to 2D scattering, lead to a singular enhancement of the nonlinear response, fundamentally dictating a natural scale of $1 \frac{μ\text{m}}{Ω\text{V}}$.

cond-mat.str-el↗

arXiv2026

Neural Network Perturbation Theory (NNPT): Learning Residual Corrections from Exact Solutions

Many complex physical systems naturally decompose into an exactly solvable component augmented by a perturbative correction. Rather than directly employing neural networks to analyze complex physical systems, we introduce Neural Network Perturbation Theory (NNPT)--a correction learning approach that predicts residual perturbations after analytically subtracting known exact solutions. Using the gravitational three-body problem as testbed, we vary Jovian mass from f=0.05 to 30 times its physical value while holding network architecture fixed. An equalized-accuracy protocol with 1% tolerance reveals an unexpected non-monotonic capacity profile: capacity peaks at f=5 in the late integrable regime (3x32, 2242 parameters), remains elevated through the transition region (f~15-17), then decreases in the fully chaotic regime (f>=17, requiring only 2x32 with 1186 parameters)--a 47% reduction from peak. With symplectic integrator energy conservation below 2x10^{-4}, this counterintuitive phenomenon reflects genuine physical structure rather than numerical artifacts. Sequential correction experiments show negligible refinement (||y2||/||y1||~0.997), confirming single-stage networks capture dominant perturbative features without hierarchical decomposition. The capacity transition at f_c=16.6+-2.8 aligns with Chirikov's resonance-overlap criterion. Intermediate-complexity regimes impose maximal capacity requirements, while fully chaotic dynamics undergo ergodic smoothing--trajectory-specific fluctuations become irreducible noise, leaving only statistically smooth corrections requiring fewer parameters.

physics.comp-ph↗

arXiv2026

Exactly solvable non-planar $\mathbb{Z}_{2}$ dimer liquids on checkerboard and ruby lattices

We generalize an influential framework for exactly solvable quantum dimer models with dual Ising gauge theory descriptions realizing the $\mathbb{Z}_{2}$ topological phase from trivalent to tetravalent parent lattices. The resulting quantum dimer models live on crossed-medial lattices and possess the remarkable feature of having crossed plaquettes, leading to transition graphs with generically intersecting loops. This non-planar structure runs counter to established templates for analytically tractable dimer liquids. As the simplest realization of the construction, we introduce an exactly solvable quantum dimer model on the checkerboard lattice that allows an exact mapping to the toric code, thus providing a particularly direct connection between the latter and Anderson's short range resonating valence bond paradigm. We further show that a corresponding crossed ruby lattice construction, dual to an Ising gauge theory on the kagome lattice, naturally falls within the same framework. More generally, the construction gives rise to a broad class of exactly solvable crossed-medial quantum dimer models and admits natural iteration, generating cascades of solvable $\mathbb{Z}_{2}$ topological dimer liquids beyond the standard planar setting. We furthermore extend Kasteleyn methods to the relevant non-planar graphs, enabling controlled wave-function deformations away from the commuting-projector points while retaining efficient evaluation of correlation functions.

cond-mat.str-el↗

arXiv2026

Signature of Unconventional Superconductivity in the High Temperature Normal State Resistivity

Unconventional superconductivity remains one of the central unsolved problems in quantum materials, and revealing its connection to the normal state is widely believed to be key to uncovering the pairing mechanism. Previous efforts have largely focused on the temperature range immediately above the superconducting transition, where specific scattering channels-such as strange-metal transport-have been identified as sharing a possible microscopic origin with superconductivity. Here, using machine learning, we demonstrate a strong correlation between normal-state resistivity and superconductivity in Fe-based superconductors. Remarkably, the predictive information reside in a wide window of 150-300 K, far above $T_c$ of this family. We further show that the signatures of superconductivity are distributed across multiple scattering channels, which requires further theoretical investigation.

cond-mat.supr-con↗

arXiv2026

Redundancy from Subsystem Thermalization

In the theory of decoherence, redundancy is the correlation between a quantum system and fractions of the environment. It underlies the emergence of classical behavior. We show that redundancy can persist despite thermalizing dynamics in the environment. This follows an initial broadcasting interaction that changes the density of a conserved quantity. The mutual information between the system and a fraction of the environment is estimated using the large deviation principle governing subsystem thermalization.

quant-ph↗

arXiv2026

Pattern Expansion of Spin Glasses

We introduce a systematic method for expanding general spin-glass Hamiltonians in terms of Mattis interactions, providing a novel perspective for understanding the fundamental differences between short-range Edwards-Anderson (EA) and mean-field Sherrington-Kirkpatrick (SK) spin glasses. By iteratively extracting patterns from the coupling matrix, we expand the original spin-glass system into a Hopfield-like model (a series of Mattis interactions) plus a residual system. Our analysis reveals profound distinctions between EA and SK models: while EA models in two and three dimensions break into isolated subconnected sections after expansion, the SK model exhibits remarkable self-similar behavior, with the residual system preserving the mean-field structure and Gaussian statistics throughout the expansion process. This self-similarity manifests in exponential decay of residual matrix norms and expansion coefficients, reflecting the inherent mean-field nature of the SK model. Furthermore, we demonstrate that pattern expansion can identify ultra-low energy excitations in EA models, revealing excitations with energies that decrease rapidly with expansion step. Through connected component analysis, we quantify the size-energy relationship of these independent excitation clusters, opening new avenues for understanding the low-energy landscape of spin glasses and providing insights into the nature of metastable states.

cond-mat.dis-nn↗

arXiv2026

Generalized Wigner theorem for non-invertible symmetries

We establish the conditions under which a conservation law associated with a non-invertible operator may be realized as a symmetry in quantum physics. As established by Wigner, all quantum symmetries must be represented by either unitary or antiunitary transformations. Relinquishing an implicit assumption of invertibility, we demonstrate that the fundamental invariance of quantum transition probabilities under the application of symmetries mandates that all non-invertible symmetries may only correspond to {\it projective} unitary or antiunitary transformations, i.e., {\it partial isometries}. This extends the notion of physical states beyond conventional rays in Hilbert space to equivalence classes in an {\it extended, gauged Hilbert space}, thereby broadening the traditional understanding of symmetry transformations in quantum theory. Our generalized theorem applies irrespective of the origin of the (non)invertible symmetry, holds in arbitrary spatial dimensions, and is independent of the Hamiltonian or action. We explore its physical consequences and, using simple model systems, illustrate how the distinction between invertible and non-invertible symmetries can sometimes be tied to the choice of boundary conditions.

quant-ph↗

arXiv2026

The Eggbox Ising Model

We introduce the Eggbox Ising model, a tunable construction of rugged energy landscapes defined by distances to a prescribed set of patterns. Correlated pattern ensembles realize arbitrary k-step replica-symmetry-breaking structures and controllable Parisi overlap distributions p(q), consistent with the hierarchical overlap structure observed in a simple word-embedding example from empirical data. A softened variant allows a systematic expansion leading to Hopfield-type couplings (and higher-body terms). We analyze the density of states and show that suitable potentials induce discontinuous finite-temperature transitions with metastability and hysteresis.

cond-mat.stat-mech↗

arXiv2026

Optimizing p-spin models through hypergraph neural networks and deep reinforcement learning

p-spin glasses, characterized by frustrated many-body interactions beyond the conventional pairwise case (p>2), are prototypical disordered systems whose ground-state search is NP-hard and computationally prohibitive for large instances. Solving this problem is not only fundamental for understanding high-order disorder, structural glasses, and topological phases, but also central to a wide spectrum of hard combinatorial optimization tasks. Despite decades of progress, there still lacks an efficient and scalable solver for generic large-scale p-spin models. Here we introduce PLANCK, a physics-inspired deep reinforcement learning framework built on hypergraph neural networks. PLANCK directly optimizes arbitrary high-order interactions, and systematically exploits gauge symmetry throughout both training and inference. Trained exclusively on small synthetic instances, PLANCK exhibits strong zero-shot generalization to systems orders of magnitude larger, and consistently outperforms state-of-the-art thermal annealing methods across all tested structural topologies and coupling distributions. Moreover, without any modification, PLANCK achieves near-optimal solutions for a broad class of NP-hard combinatorial problems, including random k-XORSAT, hypergraph max-cut, and conventional max-cut. The presented framework provides a physics-inspired algorithmic paradigm that bridges statistical mechanics and reinforcement learning. The symmetry-aware design not only advances the tractable frontiers of high-order disordered systems, but also opens a promising avenue for machine-learning-based solvers to tackle previously intractable combinatorial optimization challenges.

cond-mat.dis-nn↗

arXiv2025

Algebraic Fusion in a (2+1)-dimensional Lattice Model with Generalized Symmetries

The notion of quantum symmetry has recently been extended to include reduced-dimensional transformations and algebraic structures beyond groups. Such generalized symmetries lead to exotic phases of matter and excitations that defy Landau's original paradigm. Here, we develop an algebraic framework for systematically deriving the fusion rules of topological defects in higher-dimensional lattice systems with non-invertible generalized symmetries, and focus on a (2+1)-dimensional quantum Ising plaquette model as a concrete illustration. We show that bond-algebraic automorphisms, when combined with the so-called half-gauging procedure, reveal the structure of the non-invertible duality symmetry operators, which can be explicitly represented as a sequential quantum circuit. The resulting duality defects are constrained by the model's rigid higher symmetries (lower-dimensional subsystem symmetries), leading to restricted mobility. We establish the fusion algebra of these defects. Finally, in constructing the non-invertible duality transformation, we explicitly verify that it acts as a partial isometry on the physical Hilbert space, thereby satisfying a recent generalization of Wigner's theorem applicable to non-invertible symmetries.

quant-ph↗

arXiv2025

The Physics of Local Optimization in Complex Disordered Systems

Limited resources motivate decomposing large-scale problems into smaller,``local" subsystems and stitching together the so-found solutions. We explore the physics underlying this approach and discuss the concept of ``local hardness", i.e., the complexity of predicting local properties of the solution from local information, for the ground-state problem of both P- and NP-hard spin-glasses and related frustrated spin systems. Depending on the model considered, we observe varying scaling behaviors in how errors associated with local predictions decay as a function of the size of the solved subsystem. These errors are intimately connected to global critical threshold instabilities, characterized by gapless, avalanche-like excitations that follow scale-invariant size distributions. Away from criticality, local solvers quickly achieve high accuracy, aligning closely with the results of the computationally much more expensive global minimization. We leverage these findings to introduce a heuristic contraction-based algorithm for globally studying spin-glass ground states. The local solvers further display sharp imprints of the phase transition from the spin-glass to the ferromagnetic phase as the distribution of spin-glass couplings is shifted, as well as characteristic differences for the infinite-range model, implying the existence of specific classes of local hardness. Our findings shed light on how Nature may operate solely through local actions at her disposal.

cond-mat.dis-nn↗

arXiv2025

Lessons from $α$-RuCl3 for pursuing quantum spin liquid physics in atomically thin materials

Quantum spin liquids can arise from Kitaev magnetic interactions, and exhibit fractionalized excitations with the potential for a topological form of quantum computation. This review surveys recent experimental and theoretical progress on the pursuit of phenomena related to Kitaev magnetism in layered and exfoliatable materials, which offer numerous opportunities to apply powerful techniques from the field of atomically thin materials. We primarily focus on the antiferromagnetic Mott insulator $α$-RuCl3, which exhibits Kitaev couplings and is readily exfoliated to single- or few-layer sheets, and thus serves as a test bed for developing probes of Kitaev phenomena in atomically thin materials and devices. We introduce the Kitaev model and how it is realized in $α$-RuCl3 and other material candidates; and cover $α$-RuCl3 synthesis and fabrication into van der Waals heterostructure devices. A key discovery is a work-function-mediated charge transfer that heavily dopes both the $α$-RuCl3 and proximate materials, and can enhance Kitaev interactions by up to 50%. We further discuss a wide range of recent results in electronic transport and optical and tunneling spectroscopies of $α$-RuCl3 devices. The experimental techniques and theoretical insights developed for $α$-RuCl3 establish a framework for discovering and engineering superior two-dimensional Kitaev materials that may ultimately realize elusive quantum spin liquid phases.

cond-mat.str-el↗

arXiv2025

Emergence of a Boundary-Sensitive Phase in Hyperbolic Ising Models

Physical systems defined on hyperbolic lattices may exhibit phases of matter that only emerge due to negative curvature. We focus on the case of the Ising model under open boundary conditions and show that an ``intermediate'' phase emerges in addition to standard (high-temperature) paramagnetic and (low-temperature) ferromagnetic phases. When performing the Kramers-Wannier duality the fact that it alters boundary conditions becomes crucial, since a finite fraction of lattice sites lie on the boundary. We propose to characterize this ``intermediate'' phase by its sensitivity to boundary conditions, wherein bulk ordering is not spontaneous but rather induced by boundary effects, setting it apart from the Landau paradigm of spontaneous symmetry breaking. By developing a $\mathbb{Z}_2$ symmetry restricted extension of the Corner Transfer Matrix Renormalization Group method, we provide numerical evidence for the existence of all three distinct phases and their corresponding two-stage phase transitions, thereby establishing the complete phase diagram. We also establish how the (spontaneous) intermediate-to-ferromagnetic and the (induced) paramagnetic-to-intermediate transition points are related by the Kramers-Wannier duality relation. We discuss a holographic correspondence between boundary and bulk behaviors and derive exact expressions for boundary correlation functions on Cayley trees.

cond-mat.stat-mech↗

arXiv2025

Dilepton production from moaton quasiparticles

The phase diagram of QCD may contain a moat regime in a large region of temperature $T$ and chemical potential $μ\neq0$. A moat regime is characterized by quasiparticle moatons (pions) whose energy is minimal at nonzero spatial momentum. At $μ\neq 0$, higher mass dimension operators play a critical role in a moat regime. At dimension six, there are nine possible gauge invariant couplings between scalars and photons. For back-to-back dilepton production, only one operator contributes, which significantly enhances production near a moat threshold. This enhancement is an experimental signature of moatons.

hep-ph↗

arXiv2025

Planckian Bounds From Local Uncertainty Relations

We introduce ``local uncertainty relations'' in thermal many-body systems, from which fundamental bounds in quantum systems can be derived. These lead to universal non-relativistic speed limits (independent of interaction range) and transport coefficient bounds (e.g., those of the diffusion constant and viscosity) that are compared against experimental data.

quant-ph↗

arXiv2024

Transform then Explore: a Simple and Effective Technique for Exploratory Combinatorial Optimization with Reinforcement Learning

Many complex problems encountered in both production and daily life can be conceptualized as combinatorial optimization problems (COPs) over graphs. Recent years, reinforcement learning (RL) based models have emerged as a promising direction, which treat the COPs solving as a heuristic learning problem. However, current finite-horizon-MDP based RL models have inherent limitations. They are not allowed to explore adquately for improving solutions at test time, which may be necessary given the complexity of NP-hard optimization tasks. Some recent attempts solve this issue by focusing on reward design and state feature engineering, which are tedious and ad-hoc. In this work, we instead propose a much simpler but more effective technique, named gauge transformation (GT). The technique is originated from physics, but is very effective in enabling RL agents to explore to continuously improve the solutions during test. Morever, GT is very simple, which can be implemented with less than 10 lines of Python codes, and can be applied to a vast majority of RL models. Experimentally, we show that traditional RL models with GT technique produce the state-of-the-art performances on the MaxCut problem. Furthermore, since GT is independent of any RL models, it can be seamlessly integrated into various RL frameworks, paving the way of these models for more effective explorations in the solving of general COPs.

cs.LG↗

arXiv2024

Universal fragility of spin-glass ground-states under single bond changes

We consider the effect of perturbing a single bond on ground-states of nearest-neighbor Ising spin-glasses, with a Gaussian distribution of the coupling constants, across various two and three-dimensional lattices and regular random graphs. Our results reveal that the ground-states are strikingly susceptible to such changes. Altering the strength of only a single bond beyond a critical threshold value leads to a new ground-state that differs from the original one by a droplet of flipped spins whose boundary and volume diverge with the system size -- an effect that is reminiscent of the more familiar phenomenon of disorder chaos. These elementary fractal-boundary zero-energy droplets and their composites feature robust characteristics and provide the lowest-energy macroscopic spin-glass excitations. Remarkably, within numerical accuracy, the size of such droplets conforms to a nearly universal power-law distribution with exponents dependent on the spatial dimension of the system. Furthermore, the critical coupling strengths adhere to a stretched Gaussian distribution that is predominantly determined by the local coordination number.

cond-mat.dis-nn↗