Papers

We analyze superselection sectors, non-invertible symmetries and selection rules for RG flows triggered via perturbations of a UV two-dimensional conformal field theory (CFT$_2$). To this end we describe a method whose input is the local data, and whose output is the set of submodels of the modular invariant completions. We explain how this output set provides a classification of superselection sectors (DHR categories and Q-systems) and of topological defect lines, leading to a unified and potentially complete approach to selection rules for RG flows. This method is applied to scenarios in which the UV is a coset or a parafermion model. For these CFT$_2$ we explicitly find all submodels of the diagonal modular invariants. Our results gives selection rules that unify several known facts about such RG flows, while also allowing us to find new aspects.

Magneto-optical effects like Kerr and Faraday rotations provide a direct probe of topological order in thin films of the magnetic topological insulator MnBi$_2$Te$_4$ (MBT). Motivated by recent experimental studies of spin-flip/flop transitions in MBT thin films, we investigate the interplay between interlayer spin configurations, topological order, and magneto-optical response in five septuple-layer (5-SL) MBT using first-principles calculations and a simplified coupled-Dirac-cone model. Our results reveal that, despite possessing a non-zero out-of-plane magnetization, 5-SL MBT thin films can be either ${\cal C}=+1$ topological insulators or ${\cal C}=0$ topologically trivial insulators depending on the relative spin orientations of the top and bottom SLs. We evaluate the Faraday and Kerr rotation angles using tight-binding models derived from ab-initio calculations and by comparing our results with those of a simplified coupled Dirac-cone model clarify the macroscopic mechanisms underlying the magneto-optical response of spin-flip states. These theoretical findings highlight the tunability of topological and magneto-optical properties in MBT thin films and provide microscopic insight into the emergence of complex topological order in layered antiferromagnetic materials.

We investigate nonequilibrium dynamics and weak ergodicity breaking in a harmonically trapped spin-$3/2$ Fermi gas by using the time-dependent Hartree-Fock equation. The Shannon entropy remains bounded and oscillatory throughout the evolution, indicating restricted and nonuniform exploration of Hilbert space rather than immediate thermalization. The fidelity exhibits pronounced, nearly periodic revivals whose period is largely insensitive to particle number and interaction strength, while the revival amplitude gradually decreases with increasing system size and interaction strength. The Fourier spectrum of the fidelity reveals a set of sharp and approximately equally spaced peaks. By projecting the time-evolved state onto the instantaneous eigenbasis of the self-consistent mean-field Hamiltonian, we identify a sparse and spectrally stable manifold that forms a quasi-regular energy ladder, with spacing comparable to the dominant quasienergy interval extracted from the fidelity spectrum. These results indicate that the long-lived coherent oscillations originate from collective phase interference associated with a quasi-regular spectral structure embedded in the many-body continuum, rather than from a conventional eigenstate-dominated scar mechanism.

According to symmetrization postulate for a system of identical particles, wave function has to be completely symmetric or completely anti-symmetric. In this paper we want to mathematically justify this postulate ignoring the spin part of wave function in three dimension. For a system of N identical particles, if the solution to the governing Schrodinger equation meets these criteria: a) the probability density remains invariant when any two particle positions are exchanged over time, b) the wave function is continuous and has a continuous gradient, and the system exhibits the following characteristics: c) the configuration space, which is 3N dimensional, is connected, and d) the potential term in the Hamiltonian is invariant under the exchange of any two particle positions, then the wave function must be either totally symmetric or totally antisymmetric over time.

We report bulk magnetic properties of the monoclinic lanthanide tantalates, M'-LnTaO4 (Ln = Tb, Dy, Ho, Er), where the magnetic Ln3+ ions are arranged on a distorted 2D square lattice. The heavier analogue M'-YbTaO4 has been investigated as a spin-orbit-coupled, quasi-two-dimensional frustrated magnet, and the properties of the other M'-LnTaO4 are expected to vary depending on the electronic configuration of the Ln ion, namely Kramers vs non-Kramers behaviour and different crystal electric field parameters. In this work, powder neutron diffraction is used to confirm the crystal structure for Ln = Tb, Ho, Er, and to determine the magnetic structure of M'-TbTaO4, which displays long-range antiferromagnetic (AFM) order below T_N = 2.1 K. The Tb3+ moments are aligned primarily along the c-axis with AFM nearest-neighbour interactions. Susceptibility data suggest that M'-DyTaO4 may display short-range ordering around 2.7 K, while M'-HoTaO4 and M'-ErTaO4 show AFM correlations but do not order above 1.8 K. Measurements of the magnetic specific heat provide evidence for a Kramers doublet ground state in M'-ErTaO4, similar to its heavier analogue M'-YbTaO4.

We consider a generic model for interacting waveguide QED systems, where photons in a coupled-cavity array localize around atomic impurities while simultaneously interacting through local Kerr nonlinearities. This scenario appears naturally in nanophotonic crystals, circuit QED lattices, and ultracold atomic systems and is governed by the competition between attractive Jaynes-Cummings-mediated binding and intrinsic photon-photon repulsion. We analyze how this interplay affects the formation of localized few-photon bound states and determine the resulting many-body ground states for large periodic arrays of impurities and different filling factors. With the help of large-scale numerical simulations and approximate analytical models, we identify a rich phase diagram featuring Mott-like insulating states as well as superfluid phases with long-range correlations, which are mediated by an unbound, but strongly interacting photonic fluid.

We study the ground-state integral equation of the quantum lattice nonlinear Schrödinger model, equivalently the isotropic Heisenberg XXX chain at spin $s = -1$, whose solution is the root density on a Fermi interval. In the weak-coupling limit the equation is doubly singular: the driving term and the kernel collapse onto delta functions, and the solution separates into three regions on three scales, an inner peak, the bulk of the Fermi sea, and a boundary layer at the band edge. We treat the singular structure probabilistically. We identify both the kernel and the driving term as the Cauchy density, in such a way that the root density corresponds to the Green kernel of a Cauchy random walk killed on leaving the Fermi sea. Consequently, the three regions are then the potential kernel, the interval exit law, and the ascending-ladder renewal function of that walk. This construction determines the logarithmic growth of the central density and the digamma form of the inner profile, whose Fourier-space solution is the Bose–Einstein distribution. In the bulk, the density approaches the Green function of the half-Laplacian, while the Wiener–Hopf factorisation fixes the edge behaviour and identifies a candidate scale for non-perturbative corrections. The analysis also yields closed asymptotic expressions for the total density and the ground-state energy. Nyström solutions over a broad range of Fermi rapidities confirm the three-region asymptotic description.

The development of new-generation permanent magnets is based on experimental efforts and innovative theoretical tools for modeling magnetic properties. Magnetocrystalline anisotropy energy (MAE) - one of the main intrinsic properties of permanent magnets - can be calculated using density functional theory (DFT). However, MAEs determined with different exchange-correlation potentials can vary widely. We show how these seemingly contradictory results can be reconciled using the fully relativistic fixed spin moment (FR-FSM) method. This is because the equilibrium pairs [MAE, $m_s$] calculated with different exchange-correlation potentials overlap with the MAE($m_s$) curve determined from the FR-FSM method ($m_s$ denotes the spin magnetic moment). The FR-FSM method also enables the hypothetical maximum MAE value for a given material to be estimated. In the case of magnetic alloys, MAE(FSM) analysis allows the optimal alloying additions to be determined in order to improve the MAE value. The high independence of the MAE($m_s$) works well for exchange-correlation functionals such as LDA and GGA. However, it is not a universal measure and varies with changes in the value of the U parameter when using LDA+U or GGA+U functionals. Concluding, the framework we describe for MAE versus FSM calculations can be a useful tool in the design of new permanent magnets.

Behavior of the Grand thermodynamic potential along with its derivatives, entropy and specific heat, is considered within a two-band model of an unconventional $s_\pm$ superconductor with nonmagnetic impurities. The transition $s_\pm \to s_{++}$ is shown to be a smooth crossover at high temperatures, while it becomes the first order phase transition at low temperatures. Thus, on a phase diagram `temperature'-`impurity scattering rate' there appears to be a critical end point. Temperature at which the behavior of the transition is changed is maximal in the Born limit and tends to zero away from the limit, which points out to the possible realization of a quantum phase transition.

We study the impact of an external magnetic field on the long-range electron transport in quasi-one-dimensional materials, such as polypeptides, (semi-) conducting polymers and macromolecules, taking into account the electron-lattice interaction. At relatively strong electron-lattice interaction extra electrons get self-trapped in the deformation potential well and form stable bound states, called large polarons which in the continuum approximation are known as solitons. Here we do not use the continuum approximation but solve the system of discrete nonlinear equations numerically. We show that the impact of a magnetic field on polaron dynamics depends not only on the field strength, but also on the parameter values of the system which define the properties of solitons such as their energy, amplitude and width of localisation. We also study the impact of a magnetic field on a polaron created by a donor complex on a chain.

Equipping robotic systems with the capacity to generate $\textit{ex novo}$ hardware during operation extends physical adaptability. Unlike modular systems that rely on discrete component integration pre- or post-deployment, we envision physical adaptation through continuous in-body development via hardware synthesis. Drawing inspiration from circulatory systems that redistribute mass and function in biological organisms, we utilize fluidics to restructure the material interface, a capability currently unmatched in robotics. Here, we realize this proof-of-concept hardware generation through a vascularized robotic composite designed for programmable material synthesis, demonstrated via receptogenesis - the on-demand construction of sensors. By coordinating the fluidic transport of precursors with external localized UV irradiation, we drove an $\textit{in situ}$ photopolymerization that chemically reconstructed the vasculature from the inside out. This reaction converted precursors with photolatent initiator into a solid dispersion of UV-sensitive polypyrrole in PETG, establishing a sensing modality validated by a characteristic decrease in electrical impedance. The newly synthesized sensor closed a local control loop in real time to regulate wing flapping in a moth-inspired robotic demonstrator. Our work is a proof-of-concept materials basis for $\textit{ex novo}$ hardware generation in a vascularized composite - a step towards situated robots adapting to environmental cues.

We determine the finite-temperature phase diagram and critical behavior of the classical square-lattice Heisenberg-compass model using large-scale Monte Carlo simulations and finite-size scaling. Six symmetry distinct ordered phases are identified. The four phases that simultaneously break the spin-lattice $C_4$ and in-plane spin-inversion symmetries undergo continuous transitions in the Ashkin-Teller universality class, with the associated critical lines terminating at four-state Potts points, beyond which the transitions become first order. In contrast, the two $z$-polarized phases display conventional two-dimensional Ising criticality. Our results reveal how the interplay between Heisenberg exchange and compass anisotropy organizes these distinct critical regimes, thereby completing the characterization of the model's thermal phase transitions.

We introduce Bi$_2$CuO$_3$(SO$_4$) as a rare example of a spin-ladder magnet with ferromagnetic interactions on the rungs. Its magnetic response is studied through measurements of heat capacity, temperature-dependent magnetic susceptibility, and field-dependent magnetization, as well as electron spin resonance spectroscopy. These experiments are complemented by density-functional-theory calculations combined with the construction of maximally localized Wannier functions and an analysis of the relevant superexchange pathways. Quantum Monte Carlo simulations are employed to model thermodynamic properties and to quantitatively determine the magnetic exchange parameters. Our combined approach identifies Bi$_2$CuO$_3$(SO$_4$) as a two-leg spin-ladder system with ferromagnetic rungs ($J'$ $\approx -208$ K) and antiferromagnetic legs ($J$ $\approx 258$ K). These interactions of similar magnitude arise from remarkably different superexchange pathways, with the Cu–Cu distance along the leg being almost twice as long than the respective distance along the rung. The antiferromagnetic leg coupling represents the strongest oxygen-mediated long-range superexchange in a Cu$^{2+}$ compound reported to date and sets the benchmark for the role of complex superexchange pathways in quantum magnets.

The (2+1)-dimensional U(1) sigma model with temporal Berry phase term captures zero-temperature phase-fluctuation-driven superfluid (SF) transitions in two spatial dimensions. From renormalization group (RG) analysis of its dual representation – vortex loop gas model –, we clarify that the Berry phase leads to space-time anisotropic interference in vortex-loop proliferation, resulting in a quasi-disordered phase with short-ranged spatial yet persistent temporal phase coherence. The phase shares physical properties of the Bose glass phase known from disordered boson systems, suggesting a unified topological origin for the emergence of the glassy phase in phase-fluctuation-driven superfluid transitions.

We present a compact dynamical mean-field theory (DMFT) for large networks of coupled phase oscillators whose phases live on the circle $S^1$ and interact with both coherent mean-field coupling and quenched randomness. Starting from wrapped Langevin dynamics, we build a path-integral representation that keeps the $2\pi$-periodicity of the phases explicit. After averaging over the disorder in the thermodynamic limit, this construction reduces to a single-oscillator stochastic equation driven by a deterministic mean field and a self-consistent colored Gaussian noise, whose covariance is fixed by a circular two-time correlator. In the limit of vanishing disorder, the formalism reproduces the Ott–Antonsen reduction and recovers standard Kuramoto and theta-neuron neural-mass equations. The same framework accommodates arbitrary $2\pi$-periodic coupling functions, including those obtained from infinitesimal phase response curves (iPRCs) of biophysical neuron models. As an example, we show that for adaptive exponential integrate-and-fire neurons, inserting an iPRC-fitted coupling into the compact DMFT yields quantitative predictions for synchronization thresholds, providing a direct route from single-neuron phase response data to network-level mean-field predictions for arbitrary phase-reducible oscillators.

The Hopfield model provides a paradigmatic framework for associative memory. Its classical implementation, based on the Hebbian learning rule, suffers from catastrophic forgetting: when one attempts storing too many patterns, the network fails to retrieve any of them. Yet, the Hebbian rule does not take into account that synaptic strength is bounded. Introducing this biologically plausible modification, known as "clipping", eliminates catastrophic forgetting; the model is now able to retrieve the most recently seen memories, eliminating older ones. Yet, its memorization capacity is much reduced with respect to the unclipped case. Here, we investigate the effects of adding a "dreaming" phase on the capacity of a clipped Hopfield model. Following a proposal by Hopfield, Feinstein and Palmer, we assume that during the dreaming phase, the model generates random patterns that are then "unlearned". We show that while clipping still removes catastrophic forgetting, alternating learning and dreaming phases improves the memorization capacity and makes the search for optimal performance more realistic from an evolutionary perspective.

Structure and dynamics of a polymer under confinement gets significantly altered due to the imposed geometric restrictions. Using molecular dynamics simulations, here, we explore the effect of cylindrical confinement on the kinetics of collapse of a homopolymer, when the solvent condition is abruptly changed from good to poor. The observed phenomenology for a range of the cylinder radius $R$, reveals two distinct stages of the collapse. The first stage is highlighted by the formation and growth of local connected clusters resembling a pearl necklace, eventually ending with a single sausage-like cluster. In the second stage, the sausage-like intermediate approaches a spherical globule via surface-energy minimization. These two stages are disentangled using a shape parameter of the individual pearls or clusters, allowing us to also extract the respective relaxation times, and thereby their scaling behaviors with respect to the length of the polymer. We find that the pearl-necklace relaxation time $\tau_p$ is independent of $R$. On the other hand, the sausage-relaxation time $\tau_s$ varies inversely up to a certain $R$, beyond which it also saturates. From the Arrhenius plots of the temperature dependence of $\tau_p$ and $\tau_s$, we extract the activation energies $E_{\rm a}$ of the two stages. While the estimated $E_{\rm a}$ for the pearl-necklace stage is independent of $R$, for the sausage relaxation it is significantly higher in the strongly confined case than in the weakly one. Surprisingly, at a fixed temperature, the growth of the average cluster size obeys a universal power law irrespective of $R$. However, for a fixed $R$, the behavior is rather non-universal with respect to temperature. We propose viable scenarios for experimental realization of polymer collapse inside cylindrical nanochannels.

The cooperative effect of Rashba spin-orbit coupling (SOC) and Coulomb attraction in stabilizing topological spin-triplet excitonic condensates (ECs) in two-dimensional electron-hole systems in external magnetic field is investigated by using an unrestricted Hartree-Fock approach combined with the random-phase approximation. At weak electron-hole Coulomb interaction, the intraband Rashba SOC induces spin-momentum locking and topological semimetal behavior, while stronger interaction stabilizes spin-triplet ECs. Increasing the valence-band SOC drives a transition from a topologically trivial EC with coexisting spin-up and spin-down components to a topological spin-up EC only with quantized Chern number $C=2$. The dynamical excitonic susceptibility reveals a soft spin-up triplet mode acting as the precursor of the condensate. These results establish a microscopic mechanism for Rashba SOC-induced topological ECs and suggest realistic situations for their realization in noncentrosymmetric Janus transition-metal dichalcogenides and twisted van der Waals heterostructures.

We investigate the influence of phonon degrees of freedom on the qubit dynamics in Jaynes-Cummings (JC) model. A strong qubit-phonon coupling is considered giving rise to Jaynes-Cummings-Holstein (JCH) model. Under anti-adiabatic conditions, we perform a unitary transformation to make the underlying problem tractable through Redfield-type non-Markovian master equation. Analytical expression for the time-dependent coherence is obtained, incorporating both cavity-induced dissipation and phonon-induced dressing effects. The dynamics of JC model is highly non-Markovian for a narrow spectral width and finite detuning. However, a non-zero phonon coupling suppresses these non-Markovian features by effectively reducing the qubit-cavity interaction strength. {It is observed that polaronic dressing effectively supresses the detuning effects. Furthermore, the coherence-based non-Markovianity measure shows an order-of-magnitude suppression in the JCH model, indicating a new dynamical regime, while memory effects extend over a wider range of spectral densities than in the JC model.

We report the deterministic experimental realization and controlled fission of magnetic multi-soliton states in a uniform quasi-one-dimensional immiscible two-component Bose gas. We explore the Manakov regime, where the spin dynamics is well described by the easy-axis Landau-Lifshitz equation (LLE). The gauge equivalence between the easy-axis LLE and the attractive nonlinear Schrödinger equation (NLSE) enables the direct construction of magnetic multi-solitons from the well-known NLSE solutions. We observe the two- and three- soliton states, which exhibit robust breathing in quantitative agreement with integrable theory. By introducing a weak, localized perturbation, we controllably break integrability and induce the splitting of a two-soliton into its fundamental constituents. This process reveals the composite structure of multi-soliton states and realizes an experimental analog of the inverse scattering transform.

Topological invariants and their associated anomalies have played a crucial role in understanding low-energy phenomena in quantum field theories. In lattice gauge theory, the standard $\mathbb{Z}$-valued Atiyah-Singer index is formulated via the overlap Dirac operator through the Ginsparg-Wilson relation, but extensions to more general topological invariants have remained limited. In this work, we propose a lattice formulation of the Arf-Brown-Kervaire (ABK) invariant, which takes values in $\mathbb{Z}_8$. The ABK invariant arises in Majorana fermion partition functions with reflection symmetry on two-dimensional non-oriented manifolds, and its definition involves an infinite sum over Dirac eigenvalues that must be properly regularized. By carefully treating the boundary conditions, with and without a domain-wall mass term, we demonstrate that the ABK invariant can be extracted from Pfaffians of the Wilson Dirac operator. We further provide numerical verification on two-dimensional lattices, showing that the $\mathbb{Z}_8$-valued results on the torus, Klein bottle, real projective plane, and Möbius strip agree with those in the continuum theory.

Altermagnets are a novel class of magnets that exhibit a large spin splitting but the total magnetic moment is vanishing. This unconventional spin splitting gives rise to various characteristic phenomena, such as spin current generation. In this paper, we study the orbital-Zeeman (OZ) cross term in altermagnets. Specifically, we consider the Rashba metal and the surface Dirac cones of three-dimensional topological insulators (TIs) in the presence of the altermagnetic order parameters. For the Rashba metals, the $p$-wave order parameter exerts only a limited influence on the OZ term, whereas the $d$-wave one causes the sign change of it when the order parameter becomes sufficiently large. For the TI surface, the $p$-wave order parameter retains the step-function-type dependence of the OZ term as a function of the chemical potential ($\mu$) associated with the jump at $\mu=0$, observed in the TI surface without magnetism, but its magnitude is reduced. For the $d$-wave case, the magnitude of jump at $\mu =0$ is preserved but the OZ term decreases as increasing $|\mu|$.

The spherical version of the Hopfield model for pattern recognition is considered in the static limit. Structures inside the patterns are modeled by Gaussian random variables that reward correlation between pairs of spins in a given pattern. The free energy is derived analytically with the replica method. The overlap distribution obeys a self-consistent equation. Coming from high temperatures, a spin glass phase is entered, in which patterns and correlations appear at lower temperatures. For small enough loading capacity, also a glass phase with patterns and correlations appears.

Marginally twisted bilayer graphene having small twist angles is predicted to exhibit unique structural and electronic properties, though experimental characterization remains limited. Using scanning tunneling microscopy, we investigate such systems with twist angles of 0.06^{\circ}-0.35^{\circ}. AA-stacked regions reveal a pronounced tunneling spectral peak signifying highly localized electronic states. Conversely, AB domains display uniform multiple spectral peaks, indicative of strong lattice reconstruction and enhanced electronic homogeneity. We identify two distinct strain-induced domain walls: one exhibits a sharp -120 meV spectral peak (shear type), while the other shows distinct spectral characteristics (mixed shear-tensile type). Tight-binding calculations verify strain-driven transformations of both domain wall types and confirm direct observation of strain-mediated domain wall transitions. These results elucidate the electronic structure of marginally twisted bilayer graphene and establish strain as a control parameter for domain wall states.

Proton ordering in water ice is a paradigmatic order-disorder transition in a locally constrained system. The ice rules require exactly two hydrogens close to each oxygen, restricting the disorder to an exponentially large yet strongly correlated manifold of hydrogen-bond configurations. Within this constrained space, meV-scale energy differences drive the transition from disordered ice Ih to ordered ice XI, while distinct configurations are separated by eV-scale barriers. These barriers hinder equilibration in experiments, and efficient sampling of this space with the required energy accuracy has remained a long-standing challenge in simulation. We address this by combining a machine learning interatomic potential with loop updates that preserve the ice rules and continuous updates of atomic coordinates, enabling equilibrium sampling with ab initio accuracy and capturing configurational entropic effects. In systems of up to 360 water molecules, with over 10^6 samples retained per temperature point, the simulations reveal clear first-order transition signatures at 83 K: a negative Binder cumulant, a bimodal potential energy distribution, and a sharp step in the lattice aspect ratio. Nuclear quantum effects are estimated to lower the transition temperature by approximately 20 K, bringing the prediction closer to the experimental value of 72 K.

Controlling crystallographic orientation in quasi-van der Waals (vdW) epitaxy remains a fundamental challenge, especially for material systems located near the boundary between weakly and strongly coupled growth regimes. In such marginal systems, epitaxial selection is governed by a delicate thermodynamic competition between surface-energy penalties and interfacial interaction gains, giving rise to two archetypal limits: vdW-dominated free-epitaxy and strong interfacial coupling dominated locked-epitaxy. However, dynamically driving transitions between these regimes has remained elusive. Here, we demonstrate that external light irradiation can deterministically induce such a transition. Using the thermodynamically frustrated Fe4N/mica interface as a model system, we show that photo-excited carriers act as a chemical potentiator, significantly enhancing the interfacial chemical affinity. Within a quantitative thermodynamic description, this optical modulation increases the locking criterion (I_lock)-defined as the ratio of interfacial energy gain to surface-energy cost-beyond its critical threshold. As a result, the system switches from vdW-dominated free-epitaxy with (001) orientation to chemically locked-epitaxy with (111) orientation. Our findings establish light as a non-invasive and switchable control knob to dynamically reconfigure the interfacial energy landscape in quasi-vdW epitaxy, enabling programmable access to distinct epitaxial states beyond intrinsic material limitations.

Current deep neural networks (DNNs) used in materials modeling often lack explicit physical structure and clear analytical formulations tailored to material systems, which can limit their interpretability. In this work, we integrate Material Property Fields (MPF) with the Hopfield network architecture and propose an analytically structured DNN framework named mPFDNN. MPF provides a unified framework that represents physical properties of materials as an analytical field built upon pairwise interactions, rigorously respecting fundamental symmetries, while also enabling a physically legitimate decomposition of property distributions at the atomic level. Although the Hopfield model was originally developed for Ising-like systems, we show that its dynamical evolution strategy can be naturally extended to the MPF framework. By reformulating nonlinear interatomic interactions as "hidden neurons", MPF can be extended into a deep yet analytically tractable DNN architecture that progressively captures an increasingly connected interaction landscape. This framework also provides a unified perspective that connects linear expansions and nonlinear DNN architectures within a common interaction-based formulation. Extensive validation across diverse systems, including inorganic crystals, organic molecules, and aqueous solutions, and across multiple target properties, shows that mPFDNN achieves competitive predictive accuracy while offering a physically motivated framework for structure-property mapping in chemistry, physics, and materials science.

High-entropy alloys (HEAs) combine compositional disorder with exceptional functional tunability, yet their inherently high-density limits use in lightweight systems. Here, we introduce entropy-architected nanowire metamaterials, a class of materials that couple configurational entropy with structural porosity to achieve metal-like functionality at ultralow density. FeCoNiCrCu HEA nanowires were electrodeposited into porous templates and freeze-cast into three-dimensional “bird`s-nest“ scaffolds with densities below 1 $\%$ of the bulk metal. The resulting architectures retain a disordered face-centered-cubic phase, exhibit Curie temperatures exceeding 1000 K, and deliver thermal diffusivity ($\approx0.211$ mm$^2$ s$^{-1}$) comparable to titanium alloys. Structural and spectroscopic analyses reveal nanoscale Cu segregation that enhances magnetic ordering and thermal stability. These findings demonstrate that configurational entropy and architectural hierarchy can be co-engineered to yield lightweight, high-temperature functional materials for extreme-environment applications.

Microcanonical inflection-point analysis (MIPA) identifies third-order transitions from derivatives of the microcanonical entropy, but whether such transitions admit a direct canonical formulation has remained unclear. Here we establish a fluctuation-based canonical framework for third-order transitions through a cumulant-ratio criterion whose signed extrema define their canonical counterparts and, in the single-saddle regime, are asymptotically linked to microcanonical classification. Because the criterion depends only on energy cumulants, it avoids explicit density-of-states reconstruction and remains operational in nonequilibrium steady states. Physically, it reveals dependent and independent third-order transitions as fluctuation reorganizations around low-order transitions, namely disordered-side precursors and ordered-side restructuring. Benchmarks on Onsager's two-dimensional Ising solution, finite size Potts models, and a driven nonreciprocal Ising model show that the framework is theoretically grounded and broadly applicable.

We investigate topological phase transitions in a family of deformed $\mathbb Z_3$ toric-code wavefunctions prepared from a cluster state by local deformations and projective measurements. Their norms map to the $Q=3$ Potts model for single-parameter deformations and to a three-state Ashkin–Teller-like (AT$_3$) construction with two independent four-spin couplings in the general case. Projected entangled-pair-state (PEPS) and variational uniform matrix-product-state (VUMPS) calculations identify the toric-code (TC) phase and phases in which electric ($e$) anyons are confined or condensed. These phases are separated by critical structures with central charges $c=4/5$, $8/5$, and isolated $c=1$ antiferromagnetic (AFM) endpoints. A normalized finite-distance $e$-anyon pair-state norm provides a Fredenhagen–Marcu-type check of the confinement boundary, while the topological data of the quantum double $D(\mathbb Z_3)$ imply a topological entanglement entropy $\gamma=\log3$ throughout the gapped toric-code phase. Relative to the $\mathbb Z_2$ case, the absence of sign-change folding leaves the AFM endpoints unfolded, and the extreme deformation reaches square ice with an emergent $U(1)$ one-form symmetry, Hilbert-space fragmentation, and exact scar configurations.