Papers

The law of maximum entropy production (LMEP) is a hypothetical selection principle stating that nonequlibrium systems select the evolution paths that maximize the entropy production rate (EPR). Precise quantitative experimental tests are desirable for LMEP verification. Here we report electrical-circuit experiments on suspensions of silver particles which self-organize under electric field, form conducting paths (chains) and thus generate entropy by Joule heating. Our experiments on parallel-connected pairs of samples demonstrate a competitive relationship, thereby supporting the selection of the most efficient path. We find: (1) With sufficient voltage, a conducting chain of silver particles forms, which is a self-organized dissipative structure (SODS). (2) With two samples in parallel, usually only one can develop SODS, due to the competition effect. As one sample approaches the maximum EPR, the others EPR is near zero. This confirms the path selection principle: only the highest EPR path survives. (3) At the end of the evolution, the global EPR - i.e., the samples EPR plus the power supply circuit EPR - approaches the calculated maximum within a few percent. The deviation from the calculated maximum is slightly lower when there are two competing samples. Thus, we elucidate the dynamical physical mechanism enabling natural selection: A SODS gains a form of physical "fitness" when it establishes a pathway that efficiently suppresses the driving thermodynamic potential. As it develops and approaches the maximum EPR, the SODS modifies its nonequilibrium environment by consuming available free energy and eliminating the gradients that could support alternative pathways. This creates a selection mechanism. We also examine the global implications of the LMEP and propose that it serves as a driving mechanism propelling the hypothetical ascent of civilizations along the Kardashev scale.

CaCuSi$_4$O$_{10}$ powder was studied by differential scanning calorimetry and thermogravimetry methods in the range from room temperature to 1450$\,^{\circ}$C at heating and cooling rates of 20$\,^{\circ}$C/min. The process of decomposition of cuprorivaite, the composition and transformations of its decomposition products during successive heat treatments were also studied by powder X-ray diffraction and polarization optical microscopy techniques. It was found that CaCuSi$_4$O$_{10}$ starts to decompose by incongruent melting at a temperature of about 1020$\,^{\circ}$C, with the minimum of the endothermic DSC peak associated with this process being at 1064.4$\,^{\circ}$C. CaCuSi$_4$O$_{10}$ decomposes irreversibly and subsequent cyclic annealings up to a temperature of 1450$\,^{\circ}$C at heating and cooling rates of 20$\,^{\circ}$C/min do not cause its re-synthesis. CaCuSi$_4$O$_{10}$ transforms into a two-phase system consisting of acicular crystals of monoclinic tridymite fused with green glass with the composition CuO$\,-\,$Cu$_2$O$\,-\,$CaO$\,-\,$SiO$_2$, with the weight ratio of tridymite to glass being about $12:13$, as a result of two successive annealings up to the temperature of 1450$\,^{\circ}$C.

Type-II Weyl fermions may emerge behind the event horizon of black holes. We employ the Painlevé-Gullstrand metric to study the surface of the Lifshitz transition at the horizon, equivalent to the interface separating the type-I and type-II Weyl states. We find several analogies between the black hole horizon and the transformation of type-I to type-II Weyl fermions through the Dirac line. We analyze the symmetry-protected topological order at the Lifshitz transition originating in semimetals. The emergence of Hawking radiation in Weyl semimetals is discussed. We show that the transition state from type-I to type-II Dirac fermions can be viewed as a black-hole horizon, which exhibits unique characteristics, including a Dirac-line Fermi surface with a nontrivial topological invariant and a critical chiral anomaly effect.

Controlling the stacking and rotational registry of graphene layers provides a powerful handle on atomic-scale structural reconstructions that alter the electronic landscape at the nanoscale. In particular, this governs how massless and massive Dirac fermions coexist and interact at the monolayer-bilayer graphene interface. In the limit of marginal twist, the system reconstructs into domains of distinct vertical stacking order, introducing characteristic electronic properties and new electronic length scales, a regime that, despite its structural richness, remains largely unexplored. Here, using scanning tunnelling microscopy and spectroscopy, we demonstrate that at very low rotation angles the monolayer-bilayer graphene system relaxes into a network of three distinct stacking domains with individual electronic textures revealed through spatially resolved spectroscopic mapping and corroborated by computed local density of states. We report switching of the hierarchy of the tunnelling characteristics between Bernal and rhombohedral domains as a function of bias voltage. Furthermore, the measured spectroscopic maps exhibit theoretically anticipated domain wall 'twirling' around energetically unfavorable AAB stacking nodes, promoted by out-of-plane deformations. Our results shed light on fundamental structure-property relationships underpinning moiré-driven phenomena, opening new avenues for harnessing structural degrees of freedom in van der Waals heterostructures.

The eigenstate thermalization hypothesis (ETH) provides a fundamental mechanism for emergent statistical mechanics in isolated chaotic quantum systems, asserting that individual energy eigenstates behave as pseudorandom vectors within an energy window. This enables a complete characterization of nontrivial correlations among matrix elements in the energy eigenbasis, as described by the full ETH ansatz. Nevertheless, this description breaks down in systems exhibiting quantum many-body scars, which host non-thermal eigenstates with extensive energy. In this Letter, we address this problem by formulating the scar full ETH, which captures correlations among matrix elements involving scar states. The corresponding scaling forms and factorization properties are established using typicality arguments. Multi-time correlation functions for scar states are then organized in terms of both thermal and scar cumulants, providing a nontrivial reorganization of higher-order correlations. We numerically demonstrate the validity of this framework in the paradigmatic model of quantum scars, the PXP model. Our results pave the way for a systematic understanding of intriguing correlations in systems with quantum many-body scars.

Previous density functional theory (DFT) calculations for random solid solution (RSS) CoCrNi predict negative intrinsic stacking-fault energy (ISFE) at 0 K, contrary to experimental observations of finite stacking-fault widths. Two explanations have been proposed: finite-temperature stabilization of the RSS state, suggested by harmonic approximations showing increasing ISFE with temperature, and local chemical order (LCO), which shifts the ISFE to positive values at 0 K. Here, we compute temperature-dependent generalized stacking-fault free energies for RSS and LCO CoCrNi using a near-quantum-accuracy machine learning interatomic potential and the fully anharmonic projected average force integrator. Unlike harmonic approximations, our anharmonic calculations show that the RSS ISFE decreases with temperature and remains negative, indicating that RSS stacking faults are not thermally stabilized at elevated temperatures. By contrast, LCO maintains positive ISFE over 0-1000 K. Molecular dynamics simulations further confirm unbounded dislocation dissociation in RSS CoCrNi but finite stacking-fault widths in the LCO state.

Liquid mixtures with a nematogen can undergo both fluid phase separation and a transition from an isotropic to a nematic state. These phase transitions can couple and lead to phase behavior distinct from simple liquid mixtures or pure liquid crystals. We measured the phase behavior of mixtures of a nematogen (5CB) with simple liquid solvents (squalane and/or squalene). We observed two distinct kinds of binary phase diagrams: with and without a region of isotropic-isotropic coexistence. Varying the ratio of squalene to squalane, we continuously tuned the phase boundaries of the apparent binary system and revealed a region of three-phase coexistence. A mean-field model combining classical models of liquid mixing and nematic ordering quantitatively describes both binary and ternary phase behavior. This simple model predicts a range of topologically complex ternary phase diagrams and extends naturally to systems with more components.

The unitary Fermi gas serves as a tunable realization of a strongly coupled CFT, making it a powerful system for probing universal quantum many-body phenomena. Precise measurement of its properties remains experimentally challenging: finite-temperature effects and spatial inhomogeneity introduced by external trapping potentials can significantly distort observables. Cylindrical trap geometries are commonly used in experiments. This note extends an existing theoretical framework to this geometry, deriving how the cylindrical confinement modifies the dynamic structure factor at zero temperature. These results provide a necessary correction for the interpretation of experimental spectra in trapped unitary gases.

Looking at physical systems as computers allows us to regard physical properties, such as thermal noise, symmetry or topology, as unconventional resources for computation. However, harnessing these resources requires programming computational functionality through strong, controllable nonlinearities in the system. Here, we show that cavity optomechanical interactions allow laser-controlled computation with nanomechanical degrees of freedom. We demonstrate a set of basic digital logic gates with level restoration and controlled mechanical couplings as essential ingredients for arbitrary computing networks. Owing to the strong optomechanical nonlinearity and precise readout, the system operates close to thermal amplitudes, in the regime where thermodynamic stochasticity governs its behavior. This opens a new path for the realization of physical computing with controlled nonlinear resonators.

The development of radiation-tolerant materials capable of maintaining structural, electrical, and thermal stability in extreme, radiation-rich environments remains a critical challenge in materials science. In this work, the effects of 60 MeV 35Cl ion irradiation on highly oriented pyrolytic graphite (HOPG) and multilayer reduced graphene oxide (ML-rGO) were investigated. The samples were exposed to fluences of 5.11 x 10^9 and 1.3 x 10^10 ions/cm^2 and characterized by X-ray diffraction (XRD), Raman spectroscopy, scanning electron microscopy (SEM), atomic force microscopy (AFM), and electrical transport measurements. The results show that the irradiation response is strongly influenced by the initial structural organization of the material. In HOPG, ion exposure leads to a progressive loss of crystalline order, evidenced by XRD peak broadening and an increase in the Raman ID/IG ratio, accompanied by a reduction in electrical transport performance. In contrast, ML-rGO exhibits distinct behavior at higher fluences, suggesting partial structural reorganization. The appearance of more defined graphitic features in XRD and Raman analyses, along with changes in surface morphology and electrical response, suggests the formation of more ordered sp2 domains. These findings indicate that irradiation effects vary with the initial degree of order, providing useful insights for selecting carbon-based materials for devices operating under severe radiation conditions.

The superfluid-insulator transition in systems of lattice bosons is usually analyzed in the framework of the Bose-Hubbard model, and has been extensively studied by theory and simulations. Less attention has been paid to the remnants of the transition in truncated lattices, with or without periodic boundary conditions. Here we consider the hard-core limit of the extended Bose-Hubbard model on small square and triangular grids – i.e., sections of the square and triangular lattices containing up to 13 sites. By mapping out the zero-temperature phase diagram through exact diagonalization, we find ground-state characteristics that are markedly different from those emerging in the thermodynamic limit, together with similarities. The dichotomy between superfluid-like and insulating-like behavior is then investigated in two-dimensional systems of a few interacting bosons in the continuum, subject to confining and optical-lattice potentials mimicking the $3\times 3$ square grid. Using path-integral Monte Carlo simulations, we compute kinetic and potential energies, as well as superfluidity and exchange-cycle statistics, finding hints of Bose-Hubbard behavior even in systems of just five particles.

Recent experiments on graphene multilayers under displacement field have demonstrated a wide variety of electronically ordered phases, including valley and/or spin polarized phases as well as potentially unconventional superconducting phases. In addition, quantum oscillation measurements in Bernal bilayer graphene and rhombohedral trilayer graphene showed the presence of electronic nematic states. Here, we investigate the emergence of nematic order in these systems, with emphasis on Bernal bilayer graphene, within a self-consistent Hartree–Fock framework, using a realistic band structure with trigonal warping and a dual-gate screened Coulomb interaction. We compute the phase diagram as carrier density and displacement field are varied, and find a sequence of isospin (spin and valley) polarized states consistent with experiment, including partially polarized phases with a large Fermi pockets for isospin-majority carriers and smaller Fermi pockets for isospin-minority carriers. Within these partially isospin polarized states, we identify regions with three $C_3$-symmetric pockets for the minority carriers and regions with only one or two such pockets, implying that the system develops a spontaneous nematic order that breaks $C_3$ symmetry. We find numerically that nematicity emerges near the boundary between fully and partially polarized phases and is controlled by the strength of the screened interaction. We analytically derive a criterion for the nematic order, which agrees with our numerical results.

As CMOS technology scales down, thermal fluctuations increasingly impact circuit behavior, posing challenges to conventional circuit design. However, the inherent stochasticity introduced by thermal noise is now being explored as a potential resource in the emerging field of probabilistic computing. This work presents a fully CMOS experimental platform that enables direct control over its intrinsic thermal fluctuations. These devices function as programmable multivariate Gaussian samplers, offering a hardware primitive for energy-efficient stochastic computing and serving as an experimental platform for studies in electronic noise and stochastic thermodynamics.

We present a GPU implementation of the finite-temperature Lanczos method (FTLM) for Heisenberg spin Hamiltonians that targets workstation hardware rather than distributed-memory clusters. The Hamiltonian action is evaluated matrix-free in a row-wise gather formulation. We introduce and compare two state-to-index strategies: a compressed lookup table (CLT), which reduces lookup memory by a factor of 16 relative to a full table while retaining a fixed, branch-light access pattern, and a GPU-adapted combinatorial-ranking scheme that removes the lookup table altogether. Numerical tests against FP64 CPU references show that FP32 GPU arithmetic changes heat capacities and magnetic susceptibilities by amounts several orders of magnitude below the stochastic uncertainty of the FTLM trace estimator at typical sample sizes. Benchmarks show speedups of up to about one order of magnitude over optimized multicore CPU calculations and enable Hilbert-space sectors of dimension ~10^8 on a single workstation GPU. The MATLAB/CUDA implementation, including example input files and benchmark scripts, is openly available at https://github.com/ghasdeke/ftlm-gpu (archived at DOI: 10.5281/zenodo.20378647) under the Apache-2.0 license.

Compound-refractive lenses (CRL) are a type of x-ray optics that find widespread applications as focusing and imaging lenses. The choice of material is one of the most defining properties of these lenses. In this work, we present a CRL made out of diamond. It provides an advantageous balance between refractivity and absorption, along with good manufacturability. Compared to Be CRLs, it features a higher optical density and thus enables application at higher photon energies without relying on large lens stacks or very small radii of curvature, which are challenging to manufacture. A diamond CRL is characterized for use as an objective for Dark-field X-ray Microscopy (DFXM) at the ID03 beamline of the European Synchrotron Radiation Facility (ESRF) and compared to Al and Be CRLs at 17 keV, 33 keV and 37 keV. Increasing the photon energy in DFXM from 17 keV to 37 keV opens up the possibility to investigate new sample systems, that were previously opaque to low energy x-ray radiation. The capability of the diamond CRL at 33 keV is illustrated through DFXM measurements on two 0.5 mm-thick iron-based samples, which cannot be probed at 17 keV.

We study Krylov construction in periodically driven conformal field theories and their lattice realisations via critical fermions. Two types of driving are considered: a square-wave drive and a continuous sinusoidal drive. Using the Arnoldi construction, we examine Arnoldi coefficients and return amplitudes in periodically driven conformal field theories in the heating and non-heating phases. In the heating phase, the Arnoldi coefficients approach unity exponentially; in contrast, in the non-heating phase, they exhibit oscillatory behaviour. For the lattice realisations, we further analyse the Krylov complexity of the correlation matrix, quasi energy level statistics, and the graph structure induced by the Floquet operator. Although the two drives exhibit similar Krylov growth on the CFT side, their lattice realisations exhibit markedly different spectral and graph signatures, indicating distinct mechanisms governing the transition between the heating and non-heating phases.

Finite-temperature properties of strongly correlated quantum matter are central to condensed matter, chemistry, and high-energy physics, yet are often inaccessible to classical methods such as quantum Monte Carlo (QMC). Here, we investigate dissipative thermal state preparation of frustrated spin systems using digital quantum computers. We focus on two paradigmatic models on the kagome lattice: the antiferromagnetic Heisenberg model (AFHM), whose finite-temperature properties are inaccessible to QMC due to a severe sign problem, and the antiferromagnetic Ising model (AFIM), which serves as a sign-problem-free benchmark. Using IBM quantum processors, we prepare approximate thermal states of the AFIM on kagome lattices with up to 79 spins coupled to 60 environment qubits. We observe the emergence of a robust steady state with an adjustable effective temperature that persists in circuits with over 1000 layers of two-qubit gates. We further study the scalability of the dissipative protocol through classical statevector simulations of the AFIM and AFHM. On lattices with up to 27 sites, we find that the circuit depth to reach thermal equilibrium is independent of system size and grows at most linearly with inverse temperature. These results establish engineered dissipation as a promising approach to finite-temperature quantum simulation of frustrated matter, and point toward regimes where quantum devices may outperform classical methods.

We study the emergence of superconductivity in the one-band Hubbard model using the spin-rotation-invariant Kotliar-Ruckenstein slave-boson (SB) approach. Motivated by its intrinsically renormalized mean-field ground state, we construct an effective pairing vertex from dynamical fluctuations about the saddle point. Solving the anisotropic, frequency-dependent gap equation on the square lattice, we map the pairing instabilities across doping, interaction, temperature and real-frequency gap structure that qualitatively match experimental cuprate observations. This framework merges strong-correlation SB-type renormalizations with RPA-type pairing transparency, providing a scalable route to modeling multi-orbital superconductivity at strong coupling.

The interplay between interactions and quantum geometry can drive weakly dispersive bosons into different exotic many-body phases. In this work we study a quasi flat-band model in one dimension that exhibits an extended pair-superfluid phase in the all-flat-band limit. Introducing single-particle hopping leads to an intriguing competition with a more conventional single-particle superfluid: we find that the pair superfluid remains stable for a finite range of the hopping strength until the system eventually transitions into the conventional superfluid phase. In our study, we make use of a variational Gaussian state approach that provides a unified description of the single-particle and pair superfluid phases, regarding both the ground state wavefunction and the collective excitation spectrum. In particular, we derive a general relation between the speed of sound and a “quantum geometric kernel”, thereby extending earlier connections to the quantum metric, which relied on single-particle mean-field theory. This approach is combined with insights from the two-boson problem and exact diagonalization to map out the full phase diagram of the model. Our results show that the Gaussian approach is a versatile tool for studying a broad range of superfluid phases of interacting bosons in multi-orbital lattices.

We develop a Schwinger–Keldysh effective theory for quantum-interference corrections in a two-dimensional electron system in the hydrodynamic regime. Starting from the clean hydrodynamic fixed point, we introduce a minimal random-friction disorder model that generates a finite momentum-relaxation time within the self-consistent Born approximation. The disorder-averaged theory then allows us to construct a hydrodynamic Cooperon and to compute the associated self-energy corrections to the collective modes. Conservation laws protect the density and momentum sectors, so that the leading quantum-coherence correction is forced into the spin-two stress sector. The associated stress self-energy renormalizes the shear viscosity and modifies both the Gurzhi response and its low-field magnetohydrodynamic signatures.

We study Abelian $S$-duality of Maxwell theory on $A$-type asymptotically locally Euclidean (ALE) spaces. Unlike on closed four-manifolds, the Maxwell path integral on an ALE space is not naturally a scalar partition function. Rather, it decomposes into theta-function blocks labeled by flat $U(1)$ holonomy sectors on the asymptotic lens-space boundary. We interpret these blocks as components of the Hilbert-space boundary state prepared by the ALE path integral. With this interpretation, the apparent failure of ordinary modularity is replaced by vector-valued modular covariance under the action of the modular group. We test this picture explicitly for Eguchi-Hanson space by gluing it to its orientation reversal. The resulting closed four-manifold is diffeomorphic to $S^2\times S^2$, and the natural pairing of the two ALE boundary states reproduces the standard Maxwell partition function on $S^2\times S^2$. We then refine the construction by turning on electric and magnetic $1$-form symmetry backgrounds. In their presence, the ALE theta blocks are not ordinary functions, but sections of a line bundle over the Cartan torus associated with the $A_{N-1}$ root lattice, reflecting the mixed electric-magnetic $1$-form anomaly. We also discuss gauging discrete $\mathbb Z_k$ subgroups of the $1$-form symmetries and show that the vector-valued boundary-state structure remains the natural covariant framework after gauging. In this sense, ALE spaces behave as chiral building blocks for four-dimensional Maxwell theory: individual ALE blocks carry sector-resolved boundary data, while gluing pairs these sectors to produce an ordinary closed-manifold partition function, much like the pairing of left- and right-moving conformal blocks in two-dimensional CFT.

We show that quantum-interference corrections in an electron fluid are tightly constrained by hydrodynamic Ward identities: charge and momentum conservation protect the $m=0,\pm1$ sectors, so the leading correction first appears in the spin-two $m=\pm2$ stress sector. The resulting hydrodynamic Cooperon has a robust infrared structure that renormalizes stress relaxation, and hence the viscosity. In channel flow this lowers the viscous resistivity, producing a hydrodynamic interference signature with the opposite sign to ordinary weak localization.

Changes in the entanglement structure and critical phenomena are hallmarks of quantum phase transitions. Here, we discuss how they appear in transitions between classes of states with distinct entanglement patterns beyond the paradigm of stable equilibrium phases of matter. Using a mapping between stochastic automata and isometric Tensor Network States (isoTNS), we construct a two-dimensional quantum state from the Domany-Kinzel automaton, which is a (1+1)D process with an absorbing phase transition in the directed percolation class. At the critical point of the automaton, the corresponding isoTNS hosts algebraic correlations in all spatial directions. The continuous parent Hamiltonian of this state has a degenerate ground state manifold. It consists of a product state (the absorbing state) and a second state that undergoes a transition from pairwise entanglement between distant regions, similarly to the W state, to a state with trivial entanglement. Our results demonstrate how the correspondence between isoTNS and classical stochastic evolution can be used to probe the Hilbert space structure beyond stable ground state manifolds.

Fermionic Gaussian states describe free fermions and underlie the mean-field picture of matter, from metals to superconductors; they are also efficiently simulable on classical computers. Departures from Gaussianity – the correlations produced by interactions – are therefore what make a fermionic system hard to simulate classically and useful for quantum computation, analogous to the role of magic in stabilizer-based quantum computation. Yet detecting and quantifying such non-Gaussianity at scale has remained challenging. Here we introduce practical tests and witnesses of fermionic non-Gaussianity built on fermionic antiflatness, a measure derived from the two-point covariance matrix. We estimate it with two protocols – a two-copy Bell measurement and a single-copy scheme using commuting Majorana bilinears – that determine whether a state is Gaussian or far from it at lower measurement cost than existing approaches, using only operations native to fault-tolerant hardware. For mixed states, a purity-corrected witness certifies non-Gaussianity and remains robust under strong noise; running it on the IQM quantum processor, we find that noise can both reduce and enhance non-Gaussianity. Finally, we show that preparing pseudorandom fermionic states requires extensive non-Gaussianity. Together, these tools enable the study and certification of non-Gaussian fermionic resources on present-day quantum devices.

Twist fields are a powerful formal tool to compute Rényi entropies in quantum many-body systems, but their conventional formulation in tensor network states involves operations acting on virtual degrees of freedom, which are not directly accessible in experiments. In this work, we construct explicit local operators acting on the physical Hilbert space whose expectation values reproduce the action of twist fields in matrix product states. Our construction is exact in the injectivity limit and when the tensor is chosen at the center of orthogonality, and provides a direct operational method to evaluate Rényi entropies without accessing auxiliary tensor indices. We test our formulation numerically in the transverse-field Ising model, demonstrating rapid convergence to the exact entanglement entropy as the injectivity scale is reached. Furthermore, we show that twist operators determined from relatively small reference systems can be reliably transferred to larger systems, once the reference size exceeds a characteristic scale set by the correlation length. Since the resulting operators admit a decomposition in terms of a finite number of local observables, our results provide a scalable and experimentally accessible framework to probe entanglement in quantum simulators.

We develop a conserving relaxation-time approximation (cRTA) based on an explicit energy-resolved projection onto the full space of collision invariants. Our cRTA retains the energy dependence of the nonequilibrium quasiparticle distribution, allowing one to describe transport quantities sensitive to states near, but not exactly on, the Fermi surface (FS). We apply the method to several charge-transport problems in both Galilean-invariant and non-Galilean-invariant Fermi liquids. In particular, the cRTA reproduces the low- and high-temperature limits of the dc conductivity of a non-Galilean-invariant Fermi liquid with disorder, the hydrodynamic and collisionless limits of the finite-wavevector longitudinal conductivity of a clean Galilean-invariant Fermi liquid, and the asymptotic scaling forms of the optical conductivity of a clean non-Galilean-invariant Fermi liquid beyond the semiclassical limit. For several observables, the agreement with exact solutions is quantitative at the percent level. These results demonstrate that the cRTA provides a simple and accurate framework for describing transport beyond the FS projection.

Strong zero modes (SZMs) are edge-localized operators that commute with the Hamiltonian up to corrections exponentially small in system size, yielding anomalously long edge coherence times. In some settings, notably certain integrable models, this commutator can be made to vanish exactly at finite size, defining an exact SZM (ESZM). Existing ESZM constructions in the integrable setting, however, have proceeded model by model and have not been unified into a common framework. Here, I show that ESZMs arise generically in a broad family of integrable spin models with anisotropic interactions. Their existence follows from two algebraic properties of the underlying R- and K-matrices – quasi-periodicity in the spectral parameter and tracelessness, respectively – providing a uniform, model-independent mechanism. The framework recovers the known ESZM in XXZ chain and its higher-spin generalizations as special cases and predicts ESZMs in previously unrecognized models.

Family puzzle asks why the Standard Model (SM) features exactly 3 families of quarks and leptons. Motivated by topological constraints, we study 4d fermionic anomalies with discrete $Z_n$ symmetry, classified by the 5d spin bordism group. We show that only the group-cohomology subclass H$^5(Z_n,U(1))\cong Z_n$ can be canceled by an anomalous $Z_n$-symmetric 4d $Z_n$-gauge topological quantum field theory (TQFT), while beyond-group-cohomology $A_{Z_n}p_1$ involving the Pontryagin class $p_1$ cannot (except $n=2,3$). More generally, we prove that any cocycle $\alpha_d\in$H$^d(Z_n,U(1))$ in odd spacetime dimension $d\ge3$ is trivialised by the symmetry extension $1\to Z_n\to Z_{n^2}\to Z_n\to 1,$ and we construct the corresponding symmetric anomalous boundary TQFT. For $d=5$ and $n=3$, this yields a Spin$\times Z_3$-symmetric 4d $Z_3$-gauge TQFT that cancels the mixed discrete $(\bf B+L)$-gauge-gravitational anomaly of the SM in the absence of 3 "sterile" right-handed neutrinos $\nu_R$. We analyze a generalized SM with $N_c$ colors and $N_f$ families and argue that missing $N_f$ copies of the $\nu_R$ can be naturally replaced by a 4d anomalous $Spin\times_{Z_2^F}Z_{2 N_f,{\bf B + L}}$ symmetric $Z_N$-gauge TQFT under the anomaly cancellation, via a $Z_N$ symmetry extension construction $1\to Z_N\to Spin\times Z_{NN_f}\to Spin\times_{Z_2^F}Z_{2N_f}\to1$ of anomalous topological order. For minimal nonzero $(N,N_f)$, the allowed minimal extensions are $N=1,3,4,12$, depending on divisibility of $N_f$ by 2 and 3. Combining Witten anomaly and other constraints, we prove that $N=N_c=N_f=3$, with 3 families and 3 colors, is the unique minimal solution to match with the color-center baryon-to-quark symmetry extension $1\to Z_{N_c}\to Spin\times_{Z_2^F}Z_{2N_cN_f,{\bf Q}+N_c{\bf L}}\to Spin\times_{Z_2^F}Z_{2 N_f,{\bf B+L}}^F\to1$. We also prove that $A_{Z_3}p_1=0\mod3$ for the mod 3 cohomology class.

Density functional theory (DFT) serves as the basis for computational discovery in materials science and chemistry, yet each calculation demands extensive human effort: adjusting algorithms when convergence stalls, revising plans when unexpected physics emerges, and inserting steps as intermediate results reshape the problem. Existing LLM-based agents automate only the initial planning stage, producing a full execution plan upfront and leaving all subsequent adaptation to hand-crafted rules. As a result, these workflows remain fragile, do not generalize well beyond pre-planned scenarios, and often require expert intervention when failures or unexpected intermediate results require changes to the calculation path. Here, we introduce AutoDFT, a closed-loop multi-agent framework that embeds LLM reasoning into every stage of the DFT lifecycle, where a strategic planner produces a skeletal plan of step objectives; a step planner generates numerical parameters just in time from preceding results; and a monitor-recover-reflect cycle diagnoses failures, repairs them, and revises the plan when the evidence justifies it. We demonstrate both breadth and depth: breadth on VASPBench, a purpose-built benchmark spanning 34 tasks and 9 DFT calculation types, where AutoDFT achieves 94.1% task-level success with GPT-5.2; and depth on established materials databases, where AutoDFT produces quantitatively reliable property predictions across electronic, magnetic, and energetic properties. By closing the loop between planning and execution, AutoDFT enables experimentalists without deep computational expertise to obtain reliable first-principles results.

Commuting Hamiltonians lie at the boundary between classical constraint satisfaction and quantum many-body physics, exhibiting rich quantum structure while remaining more tractable than general noncommuting models. In contrast, physical Hamiltonians are rarely exactly commuting, which naturally motivates the study of almost commuting Hamiltonians. Despite their relevance, the implications of approximate commutation are only poorly understood. In this work, we show how to efficiently approximate any almost commuting $2$-local qubit Hamiltonian by a commuting one: we give a new locality-preserving algorithmic rounding technique that maps any $2$-local Hamiltonian $H=\sum_{i=1}^m h_i$ with $\|[h_i,h_j]\| \leq \epsilon$ to a nearby Hamiltonian $\hat{H}$ whose terms pair-wise commute, and which is within overall distance $\|H-\hat{H}\| = O(m\,\epsilon^{1/3})$. As a consequence, we show that $\delta$-approximations to the ground energy for $\epsilon$-almost commuting $2$-local qubit Hamiltonians lie in $\mathsf{NP}$ when $\delta \gg m\epsilon^{1/3}$, extending the classical containment well beyond the commuting setting. Finally, we present two applications of our rounding framework: Gibbs sampling and fast Hamiltonian simulation for almost commuting systems.