Papers

Machine learning has transformed materials simulation by delivering force fields with ab initio accuracy, yet bridging the gap between high-dimensional regression and physical interpretability remains a grand challenge. Conventional analytical potentials offer transparency but often fail to capture the complexity of far-from-ground state regimes. Here, we introduce a hybrid symbolic-neural framework that unifies the interpretability of the Embedded Atom Method (EAM) with the adaptability of data-driven learning. Using Equation Learner Neural Networks (EqNNs) trained on density functional theory (DFT) data, we obtain interpretable models for aluminum through three distinct training protocols: random initialization trained via Monte Carlo Tree Search (MCTS) and gradient descent, and two transfer-learning strategies initialized from a copper potential - one employing MCTS followed by gradient descent, and the other using gradient descent only. We find that while all three resulting symbolic models achieve sub-10 meV/atom accuracy, they occupy distinct local minima in the functional landscape, exhibiting complementary trade-offs across phonon dispersion, surface energetics, and elastic response. By integrating these diverse functional forms through a weighted symbolic ensemble, we derive a composite potential that surpasses the fidelity of its constituent models. The resulting ensemble effectively mitigates individual biases, delivering superior consistency with DFT benchmarks across equation-of-state curvature, phonon spectra, and melting dynamics. This approach demonstrates that combining transfer learning with ensemble symbolic regression yields compact, transparent potentials capable of robust prediction across equilibrium and non-equilibrium states.

We investigate how unsupervised machine-learning methods can characterize the active-absorbing phase transition in the contact process in one and two spatial dimensions. Our analysis focuses on principal component analysis (PCA) and variational autoencoders (VAEs), and we show that direct applications of these methods encounter a central difficulty: contact process configurations are intrinsically positive-definite. In the PCA case, standard centering procedures fail to isolate the order parameter in the leading component. To address this, we augment the data with sign-reversed configurations, creating a balanced dataset with zero mean while preserving the density information required to describe the transition. This preprocessing allows the dominant principal component to recover the order parameter and reproduce the expected finite-size scaling near criticality. For VAEs, we find a related limitation: a fixed Gaussian prior does not provide sufficient latent regularization across the full range of control parameters and system sizes for positive-definite data. We overcome this by adopting a heteroscedastic Gaussian prior that adapts to the control parameter, leading to a substantial improvement in the finite-size scaling of reconstruction-based observables near the critical threshold. Taken together, these results highlight a key lesson: the success of machine learning in phase-transition problems does not rely on algorithmic complexity alone, but on tailoring the representation to respect the physical structure of the system, including its intrinsic constraints and symmetries.

The pace of evolution depends on how rapidly new phenotypes arise. We show that neutral Wright-Fisher evolution exhibits anomalous first passage despite diffusive mutations. The mean time for the first individual to reach a prescribed phenotypic distance scales approximately as $(\sigma^2)^{-3/2}$ with mutation variance $\sigma^2$. Two crossovers bound this regime, with inverse-variance scaling on either side. Combining coalescent theory with Kardar-Parisi-Zhang (KPZ) fluctuations at the dilute population edge, we develop an edge-KPZ theory of all three regimes. The anomaly persists under weak selection.

We develop a two-dimensional inviscid model for extensible membranes with continuous vortex shedding from both edges, coupled to a weak spectral Galerkin discretization of the membrane equation that permits direct computation at zero bending rigidity. Viewing the pressure jump as a flux for bound vorticity explains how membranes respond to concentrated fluid loading. For fixed-fixed membranes, compliance draws the body toward the leading-edge vortex, delaying its detachment and enhancing lift primarily during start-up; after periodic shedding develops, compliance mainly amplifies the force oscillations rather than mean lift. Vortex detachment can unload heavy membranes into compression, producing bending-regularized wrinkles. For $R_2>0$, the membrane equation remains well-posed independently of the sign of the tension, provided the membrane remains an immersion. Releasing the trailing edge creates an intrinsic degeneracy: the tension vanishes at the free endpoint, making the $R_2=0$ problem formally underdetermined, while the weak formulation selects its bounded-energy branch. This vanishing-tension endpoint traps pressure disturbances and drives rapid tip-snapping; the dominant frequency and effective wave number approach their zero-rigidity limits with an inverse-logarithmic correction arising from a singular Bessel branch. Finally, decreasing the stretching modulus destabilizes periodic flutter, and the repeated fluid-driven departure and elastic return suggest a homoclinic tangle underlying the transition from periodic to chaotic flutter.

Electronic states with coexisting Wigner-crystal order can sometimes exhibit a quantum Hall effect over a finite range of electron densities—i.e., exhibit “extended” quantum Hall (QH) plateaus in the absence of disorder. Such an extended quantum Hall state can then compete with other QH states over the same density range, allowing a first-order thermal transition between them. Here, we analyze several settings in which the entropy associated with Goldstone modes (e.g., magnons or phonons) or soft gapped modes (e.g., magnetoroton) drives a finite-temperature transition between competing QH regimes. Applying this framework to moiré rhombohedral graphene, we argue that a soft magnetoroton in a fractional quantum anomalous Hall state provides a plausible bulk mechanism for the observed thermal evolution from an extended integer QH to a fractional QH regime.

Materials design must reconcile competing functional requirements with stability and synthesis constraints. Generative models can produce stable, novel crystals, but accommodating detailed natural-language design instructions remains challenging. Here we introduce HiMatGen, a framework for scaling large language model agents through hierarchical collective reasoning. Built from GPT-5.6 Terra, HiMatGen connects 100 investigators in discussion pods across ten scientific domains with tool-enabled domain representatives. Representatives investigate proposals, exchange evidence across domains and return findings and unresolved questions to their pods. This bidirectional exchange turns specialist disagreements into structural revisions and alternative designs. Across six chemical systems, HiMatGen produces 1.9 times as many final crystal candidates and 1.7 times as many stable, unique and novel (SUN) structures as a tool-enabled GPT-6 Astra single-agent baseline. In property-directed tasks, the complete HiMatGen workflow outperforms same-model single-agent and independent-generation controls. Comparisons with MatterGen and Chemeleon2 demonstrate its ability to develop diverse crystals satisfying joint functional and chemical requirements. In a paired comparison initialized from the same proposals, hierarchical discussion reduces debate-stage token usage by a factor of 22 relative to full debate. HiMatGen provides an approach to materials design that sustains the exchange of scientific knowledge and computational evidence throughout iterative exploration as the agent population grows.

Scientific literature contains latent knowledge about materials behavior, but much of this knowledge is expressed through words, contexts, and recurring associations rather than explicit design principles. This raises a central question: how can large-scale scientific corpora be used for practical problems in materials discovery? Here, we present a literature-guided descriptor-based filtering framework for reducing composition search spaces. For a given performance metric, the framework selects two descriptors from a filtered vocabulary in a literature-trained word embedding model and uses the selected descriptors to construct a Pareto-based filter for candidate compositions. Across the evaluated performance metrics and composition search spaces, the framework filters out an average of 74.27% of the candidate compositions, with an average best-value error of 1.93% relative to experimental measurements. Compared with expert-chosen and random descriptors, our performance metric-dependent descriptors provide a more controlled balance between retained fraction and best-value error. These results show that literature-derived embeddings can support intuitive and reproducible filters for narrowing candidate composition spaces while preserving high-performing compositions.

We prove blue percolation in the Chayes-Machta-Redner representation of the zero-field Edwards-Anderson spin glass in finite dimensions. For fixed symmetric iid couplings with $0<m=\mathbb{E}|J|<\infty$, the first blue-percolation inverse temperature $\beta_{\mathrm{b}}(d)$ satisfies $2dm\,\beta_{\mathrm{b}}(d)\to1$ as $d\to\infty$, in periodic joint limits. For symmetric $\pm1$ couplings, both overlap signs percolate at explicit temperatures in every dimension from 7 to 12. That proof reveals the overlap field, shows that it dominates a weakly coupled Ising field, and bounds a weighted second moment of open paths; in dimensions 7 to 9 the paths make short lateral excursions, and an interaction-matrix criterion controls the second moment. These proofs are computer-assisted: finitely many inequalities between rigorously bounded quantities are decided in exact rational arithmetic. For exponential-moment disorder, we also establish a percolating regime with exactly equal infinite-blue-sector densities and finite spin-glass susceptibility. In these periodic limits, persistent density imbalance would imply distinct spin-flip-related Gibbs states and ordinary spin-glass order: positive spatial-overlap variance, infinite spin-glass susceptibility and a cusp of the replica-coupling pressure, without requiring finite-blue cancellation. Proving imbalance remains open.

Testing an artificial system for a property linked to consciousness means applying a measurement developed on brains to a system that is not one. Such a transfer must re-examine five parts of the procedure: the competing statistical models, how they are fitted, the unit the inference generalizes over, the quantity the uncertainty interval is about, and the rule that turns a result into a verdict. The Cross-Substrate Access Assay declares all five. Because brain and model signals share no physical scale, every model is scored by the cross-entropy it assigns to held-out data, in nats per trial. The test case is the global neuronal workspace theory, which predicts that near threshold a stimulus either enters a capacity-limited workspace or does not, so that single-trial responses form a mixture of two states. A published test of this prediction on twenty people's electroencephalograms partly reproduces in a re-implementation: the first crossing and the broad ordering over time match, the window-by-window agreement does not. On 12,000 synthetic datasets generated with a single graded state, all of them members of the families the procedure fits and none within 0.0067 nat per trial of the decision boundary, the two models of that test carried over unchanged reported two states in 989 and the expanded families in none; on 600 datasets carrying a mixture the expanded procedure reported two states in 599. Its nominal 95% interval contained the procedure's mean result less often than the required 90% at six of twelve graded settings. No claim about experience is made.

Nonextensive Bose and Fermi state is well studied with counting near black-hole horizons in a one-function, nonextremal, static, spherically symmetric class. The calculation is organized around a $q$-deformed grand ensemble whose total partition function is a $q$-product of single-level partitions. This identifies the bosonic occupation-number sum as the primary level partition and allows us to separate two operations that are often conflated: replacing that sum by a geometric-series form and applying the ordinary reciprocal-log identity to a $q$-logarithm. A finite-energy tunneling prescription yields a leading near-horizon state-counting term controlled by the surface gravity and a horizon-response factor. Entropy matching then gives an energy scale proportional to the Hawking temperature; the geometry factor cancels from normalized nonextensive corrections and from the Bose–Fermi ratio. We derive the first-order coefficients analytically and evaluate the unexpanded $q$-integrals numerically. The linear approximation is accurate to better than one percent when $q$ lies within roughly two percent of unity. All prescriptions recover the extensive limit, but the exact bosonic level sum and the geometric approximations give opposite signs for the leading deformation of the conventional $7/8$ Bose–Fermi relation. The result isolates a robust geometry-factorized structure and quantifies a distinct $q$-algebra systematic uncertainty.

Standard real-time time-dependent density functional theory (RT-TDDFT) couples light to matter through a spatially uniform (dipole) vector potential, an approximation that breaks down in the X-ray regime, where the photon wavelength approaches interatomic scales. We present an all-electron, numeric-atom-centered-orbital implementation of full minimal coupling in FHI-aims that retains the spatial structure of the vector potential in both the paramagnetic and diamagnetic couplings, implements a reciprocal-space-resolved current diagnostic, and extends the propagation to periodic systems through a perturbative photon-momentum sideband coupling that recovers the density response at the photon wavevector. Four benchmarks ranging in energy from 100 eV to 5 keV validate the implementation and exercise its reach. The retained photon momentum proves physically consequential throughout, from measurable beyond dipole corrections to the enabling of channels forbidden in the dipole limit. On an all-electron footing, the implementation lays the groundwork for a general ab initio treatment of X-ray light-matter interaction across molecules, surfaces, and solids.

It is known that the Sachdev-Ye-Kitaev (SYK) model is exactly solvable at leading order in $1/q$; specifically, the instantaneously thermal time block after the quench is known in closed form. Thus far the remaining (inherently out of equilibrium) blocks have only been numerically accessible. Here we provide their analytical solutions for a quench between non-commuting $q/2$-body SYK Hamiltonians. We obtain the Green's functions in closed form for every time block. We extract a simple relation between the pre- and post-quench energies $\epsilon_1 \propto \epsilon_0$ leading to an exact temperature update rule. Via a Cauchy-Schwarz inequality, we show that heating is inevitable for the closed system; hence, the second law emerges geometrically. The solution is used in a companion paper to address what “instantaneous thermalization” means at finite $q$.

We present a highly parallelizable, matrix-free, real-space method for computing the random phase approximation (RPA) correlation energy within Kohn-Sham density functional theory. In particular, we avoid the explicit construction and eigen-decomposition of the response function matrix and use Lanczos quadrature to evaluate the trace of a matrix function on a real-space grid. We also show it is possible to exploit the spatial smoothness of the RPA correlation energy density in real-space to reduce computational cost. Specifically, we compute the energy density on a coarse grid, then reconstruct an approximation to the full, fine grid via interpolation. We implement this formulation within the SPARC electronic structure package and demonstrate its convergence, accuracy, agreement with planewave results, and scaling. Interpolation can enable an $8\times$ reduction in the computational prefactor. Given the embarrassingly parallel nature of the proposed method, we achieve near-ideal speedups and near-cubic scaling, thus allowing us to compute the RPA correlation energy for a silicon system with 256 valence electrons at chemical accuracy in less than 30 minutes on 4,096 CPU cores.

We explore the heat-rectification properties of a two-phase fluid confined in a nano-chamber with one wall coated with end-grafted polymers using molecular-dynamics simulations. We find a significant thermal diode effect for a wide range of chamber fillings for both very stiff and fully flexible polymers. A stationary heat flux is imposed on the system by fixing the walls at two different temperatures, computing the heat flow as a function of the filling density. The fluid presents a liquid phase, located close to the cold wall, and, for many fillings, a vapor phase in contact with the hot wall. A vapor-liquid interface is also present and located at different distances from the walls, depending on the fluid filling. We study the system by comparing two operational modes: a direct mode, in which the polymers are grafted on the hot wall and exposed to the vapor phase. In the inverse mode, the wall temperatures are swapped and the fluid rearranges to adapt to the interchanged temperature gradient. We calculate the mean heat flow, number density and temperature profiles for the stationary state in both modes. From them, we computed the density and temperature profiles, heat rectification coefficient, and resistivity profiles, for the two studied extreme cases of polymer bending rigidity. We found that, the nano-chamber presents a significant degree of heat rectification with different characteristics and filling density ranges. We describe the conditions to be met to obtain high thermal rectification as regards fluid filling, polymer properties and fluid-polymer affinity. They can be fine-tuned according to the application or material availability. In the direction parallel to the walls the system is easily scalable towards macroscopic sizes, without affecting the thermal rectification. This makes the soft-diode mechanism very versatile in geometry, size and materials choice.

Visible dynamics and mean dissipation need not determine the collective phases of rare histories. We construct local Markov models with identical ordinary visible path distributions, stationary states, mean entropy production, mean jump activity and driving affinities, yet different phases when histories are weighted by their full entropy production. Visible configurations modulate hidden driven cycles, whose exact elimination turns kinetic correlations into interactions. A positive spectral reduction separates hidden relaxation from collective modes. Periodic binary models retain opposite phases with entropy variances matched at every observation time. For conserved particles, a pair matches the first two joint cumulants of entropy and hidden activity at every observation time, yet selects segregation or a fluctuating state with suppressed long-wavelength density noise. Bound-state transport and fermionic evolution determine their contrasting dynamics. At a clean Ising critical midpoint, the entropy source couples quadratically to the thermal perturbation, making the fourth cumulant the first to detect the critical susceptibility. Its rate per site grows logarithmically, with an exact cutoff set by system size and observation time. For two quenched disorder ensembles, exact sample-response formulas and numerical evidence support a finite fourth-cumulant density despite very slow relaxation; a weak-disorder continuum response admits a controlled Borel sum. A common positive hidden eigenvector characterizes autonomous selected dynamics. When this condition fails, a finite network develops visible memory while preserving its ordinary visible process and mean diagnostics. These results identify kinetic information missed by aggregate thermodynamic observations.

Additively manufactured soft-magnetic Fe–Co is consistently harder than wrought material of the same composition, and controlling that excess is the central obstacle to printing electrical machines from these alloys. The literature attributes it to B2 chemical ordering, untested because the anisotropy of the ordered state had not been measured for this alloy and because printed material had never been compared with wrought material at matched grain size. In this study we supply both. Calibrating on wrought Fe–49Co–2V at a known order parameter fixes the ordered-state domain-wall energy and caps every pinning channel independent of grain size. Ordering then falls orders of magnitude short of the measured excess, and a tenfold change in antiphase-domain size leaves coercivity unchanged. What ordering controls is the wall energy, and that effect is small and bounded. The excess is retained defect content, which moves process optimization from post-build annealing to in-build defect control.

Van der Waals heterostructures offer a direct way of combining two-dimensional (2D) materials with different electronic properties, such as 2D semiconductors, metals, and superconductors, in a single device. Bilayer graphene (BLG) is particularly attractive in this context, as its electrically tunable band gap enables local control of tunnel barriers and quantum dots. Here, we realize an all-2D hybrid platform based on BLG proximitized by superconducting NbSe$_2$. Using local electrostatic gates, we define tunnel barriers and quantum dots at different distances from the lateral superconductor-semiconductor interface. The quantum dots serve as local spectroscopic probes of the proximitized BLG channel segment, forming tunable superconductor-quantum dot-normal conductor junction devices. Coulomb blockade and finite-bias spectroscopy reveal a proximity-induced superconducting gap of up to $80\,\mathrm{\mu eV}$ and allow to track its evolution with increasing distance from the NbSe$_2$ contact. We find that the local density of states remains suppressed over distances exceeding 1 $\mu$m, consistent with superconducting proximity through a highly ballistic BLG channel. Our results show that BLG-superconductor hybrids offer a controllable platform where quantum dots and quantum point contacts can be well combined with superconductivity.

In this work, we present an improved version of the formulation of the four auxiliary bosons originally proposed by Kotliar and Ruckenstein, adapted to describe a quantum dot in the Kondo regime with finite electron-electron interaction U. The proposed refinement provides a more accurate treatment of strong electronic correlations while preserving the analytical tractability of the original approach, thereby enabling a reliable description of transport properties in nanoscale systems. Benchmark calculations show good agreement with the results of the numerical renormalization group, supporting the validity of the improved formulation. Our approach therefore provides an efficient and robust framework for investigating transport through strongly correlated quantum dots.

The sign-structure of a quantum many-body ground state is a central quantity in fixed-node approaches to mitigating the Fermion sign problem. For continuum electronic-structure Hamiltonians, the correct sign-structure is sufficient to compute exact ground state properties; on the other hand, lattice fixed-node approaches retain an additional dependence on trial wave-function amplitudes which are improved upon non-optimally while preserving their sign structure. Here we consider an iterative map obtained by repeatedly replacing the fixed-node trial state with the ground state of its associated lattice fixed-node Hamiltonian (independent of whether and how a practical algorithm could implement this iteration). We show the fixed points of this map are eigenstates of the Hamiltonian and reduced Hamiltonian resulting in at most one fixed point in the interior of each sign chamber. We prove that the ground state fixed point is stable and that the boundary of the ground state sign chamber is repulsive. This shows the amplitude dependence beyond having the correct ground state sign-structure disappears under self-consistent iteration. In other sign chambers, energy descent can be obstructed by the imposed sign structure; this tension leads to the iteration driving select amplitudes to zero producing `support collapse' onto chamber boundaries and corresponding to reduced Hamiltonians. Excited-state fixed points are therefore provably unstable and flow toward lower-energy boundary fixed points. We show sign chamber boundaries have a directional stability; boundary points attractive in one direction are repulsive under a sign flip. By revealing the geometry and stability structure of iterative fixed-node dynamics, our results clarify the foundations of a central approach to the Fermion sign problem and motivate potential new algorithmic strategies.

The results of measurements of the transverse voltage in the Hall configuration, Uy, under conditions of motion of the charge and vortex subsystems in orhtogonal magnetic and electric fields on epitaxial films of the layered high-temperature superconductor Nd2-xCexCuO4 are presented. the motion of Josephson vortices across CuO2 layers (along the c-axis) is analyzed considering the effects of intrinsic pinning. An exponential dependence of critical depinning current jc(B) for Josephson vortices is established in contrast to the power law dependences for Abrikosov vortices. With increasing external magnetic field after the depinning by a magnetic field at B=Bc, the onset of the vortex creep regime, which evolves into the flux-flow regime at crossover field B=Bf, is observed.

Controlling the charge and spin degrees of freedom of electrons in solids has been at the heart of condensed-matter science for centuries. One hallmark of metallic conduction is the Wiedemann-Franz law which implies that a moving charge carries entropy. Despite centuries of dedicated research, disentangling charge and heat transport has remained an unsolved issue so far. Here we present a direct route to reduce thermal conductivity of conduction electrons with respect to their electrical conductivity via energy-dependent scattering. By constraining electronic transport to a boxcar-type distribution asymmetrically around the Fermi energy, a large Seebeck coefficient and electrical conductivity can be realized simultaneously while electronic heat conduction is suppressed. Based on the case of monolayer Ni$_3$In, which comprises two flat bands around the Fermi energy, we propose flat-band systems as a promising, tunable platform for scattering phase space engineering. Besides this novel approach, our large-scale assessment of $\approx 5\times 10^4$ data sets in a 'Wiedemann-Franz plot' of $zT$ vs. $S^2$ provides an effective tool to identify reports of $L\ll L_0$ from literature - pointing towards either new and interesting physical mechanisms - or overlooked measurement artifacts.

Manufacturability is one of several constraints on developing solid-state quantum processors, along with qubit performance, control, connectivity, cryogenic operation, and fault tolerance. Chemical residues, structural disorder, and non-uniform interfaces introduced during fabrication can compromise qubit coherence. Two-dimensional (2D) materials, with their atomically thin crystals and van der Waals interfaces, offer routes to address some of these challenges. Their concurrent development as next-generation CMOS channel materials motivates an examination of whether relevant processes can be transferred to quantum chips. This Perspective evaluates the opportunities and limitations of 2D materials for CMOS-compatible quantum hardware.

Retarded thermal correlators, analytically continued to complex frequency, exhibit non-hydrodynamic poles and branch cuts that constrain hydrodynamics. We construct Gaussian Schwinger-Keldysh effective actions in which branch cuts arise from continua of relaxation poles and response functions are governed by Stieltjes transforms of relaxation-time densities. Dynamical KMS symmetry, positivity and stability constrain the spectra, while endpoint behaviour controls the local branch structure and near-edge pole scaling. The illustrative examples of uniform and power-law densities exhibit respectively beyond-all-orders pole-endpoint separation and a continuous interpolation between pole-pole and pole-branch-point termination. Finally, we show that an energy-dependent relaxation-time approximation in kinetic theory provides a microscopic realization of our branch cuts at zero momentum.

We provide an analytic realization of spontaneous parity and time-reversal breaking without thermal restoration in a local, unitary, ultraviolet-complete quantum field theory in $2+1$ dimensions with finitely many fields. The theory is defined by a relevant Yukawa deformation of a product of the critical biconical vector model and free massless Dirac fermions. This deformation induces a renormalization group flow whose infrared endpoint is a decoupled product of the critical vector model and the conformal Gross-Neveu-Yukawa model. At zero temperature, the vacuum preserves both symmetries, whereas upon heating, the theory undergoes an inverse thermal transition at a finite critical temperature. Above this temperature, a fermion mass, odd under parity and time reversal, is dynamically generated, and the broken phase persists to arbitrarily high temperatures.

We study the classical simulability of open quantum dynamics using random Clifford circuits doped with non-Clifford phase rotations and subject to local noise. We unravel the dynamics into stochastic quantum trajectories simulated with Clifford-augmented matrix product states, and introduce a simulation cost that quantifies the classical resources required. Optimizing this cost over stochastic unravelings, we identify noise-induced classical phases: extended parameter regions in which the dynamics can be fully disentangled by Clifford operations at arbitrary circuit depth. Their existence depends on both the noise model and the unraveling. Using a geometric representation of quantum channels, we analytically determine optimal unravelings for a broad class of noise models, with numerical simulations confirming the predicted phase boundaries. We further relate the optimal cost to the unraveling-independent nonstabilizerness of the channel and show that, together with trajectory-resolved entanglement and nonstabilizerness, it classifies distinct dynamical regimes. Finally, we show that these classical phases disappear in the averaged density-matrix description, where no unraveling freedom remains. Our results show that the emergence of classicality in noisy random circuits depends on the measurement scheme adopted to probe it, and paves the way to further studies on the classical simulability of driven-dissipative dynamics.

Completeness is widely recognized in quantum information as an important property of a family of monotones, because it ensures that no information relevant to state conversion is lost. We show that completeness is also physically important in many-body systems: an incomplete measure of symmetry breaking can miss essential features of symmetry-restoration dynamics. We study the logarithmic characteristic function (LCF), also known as the string order parameter, whose full family is complete for exact i.i.d. pure-state conversion under symmetry-preserving operations for finite groups. We introduce a fidelity-based extension of the LCF to mixed states and identify two concrete advantages over entanglement asymmetry (EA). First, for a finite symmetry group $G$, EA is bounded by $\log |G|$ and can approach the same saturated value for different initial states in the thermodynamic limit, making their relaxation curves indistinguishable and preventing the identification of a discrete-symmetry Mpemba effect. By contrast, the LCF can remain extensive, with a coefficient that depends on the initial state and time, and therefore continues to distinguish their relaxation dynamics. Second, different LCF components can exhibit distinct relaxation and crossing behavior, including cases in which EA shows no crossing. We demonstrate these advantages in spin-chain quenches and a single-qubit system under depolarizing noise. We also develop a replica construction for the fidelity-based LCF in quantum field theory and derive analytical results for conformal field theory.

We study the fate of quantum solids with a vanishing velocity of transverse phonons. Such “floppy” solids exhibit a cubic elastic nonlinearity that is relevant in spatial dimensions $d<4$ and drives the system to a strongly-coupled Lifshitz quantum critical point in $d=3$, that we analyze in an $\epsilon = 4-d$ expansion. The associated phase transition is generically first-order, preempting the system's full access to the strongly-coupled fixed point. Nevertheless, the critical data of this quantum critical point is accessible within a Ginzburg region in the vicinity of the transition. This cubic nonlinearity vanishes exactly in $d=2$, where the leading interactions are instead quartic and are marginal, leading to weak logarithmic singularities. We discuss possible realizations of this “crystal Lifshitz criticality” in quantum materials.

The discovery of high-$T_c$ superconductivity in multilayer nickelates has stimulated intense interest, yet the microscopic origins of their correlated states remain debated. Recently the observed isotope effect of the magnetic state in trilayer nickelates highlights the important role of lattice vibrations in shaping these systems. Here, we investigate the impact of electron-phonon coupling (EPC) on magnetism and superconductivity in trilayer nickelates using ab initio and functional renormalization group calculations. We identify out-of-plane oxygen breathing modes with pronounced EPC and construct symmetry-resolved, layer-dependent couplings. Their relative phases across the three layers generate distinct retarded interactions, producing mode-selective enhancement or suppression of spin-density-wave order and $s_\pm$-wave superconductivity. This selectivity arises from screening-mediated spin-phonon interplay across a hierarchy of energy scales: EPC modifies charge screening at higher energies, reshapes magnetic fluctuations at lower energies, and ultimately influences pairing. Selected modes yield negative isotope coefficients for the magnetic state, qualitatively consistent with experiments. Our results establish how interlayer phonons modify electronically driven order and provide a microscopic framework for understanding isotope effects in trilayer nickelates.

We investigate the utility of the locality-preserving Derby-Klassen (DK) fermion-to-qubit mapping [arXiv:2003.06939] for variational quantum simulation of two-dimensional $t$-$V$ and Fermi-Hubbard models. The DK mapping preserves the locality of fermionic interactions with an enlarged Hilbert space, thereby requiring additional constraints that define the physical sector. We incorporate these constraints directly into a Hamiltonian Variational Ansätz (HVA) through Clifford-gate state preparation and use the Variational Quantum Eigensolver (VQE) to show that the low-energy properties of the resulting qubit Hamiltonian are accurately reproduced. We further exploit particle-number conservation inherent in the ansätz to resolve distinct symmetry sectors and reliably access degenerate states. Consequently, we benchmark the DK-HVA against Jordan-Wigner-based variational circuits at nonzero chemical potential, where particle-hole symmetry and the associated half-filled sign-free condition are absent. Finally, we demonstrate the advantage of locality-preserving mappings in higher-dimensional fermionic systems, where the conventional Jordan-Wigner (JW) transformation generates increasingly long Pauli strings and corresponding circuit overheads. We further extend the framework to the spinful Fermi-Hubbard model and identify a tradeoff between fermionic-mode placement and the locality of hopping and on-site interaction terms. These results establish a practical framework combining locality-preserving fermion-to-qubit mappings, constraint-preserving Clifford state preparation, and symmetry-preserving variational circuits, that trades auxiliary-qubit and stabilizer-preparation overhead for reduced operator nonlocality, providing a practical route toward resource-efficient quantum simulation of higher-dimensional interacting fermionic systems.

We show that an $O(1)$ local defect is sufficient to generate approximate unitary $k$-designs from an otherwise integrable quantum many-body system. Using a two-Pauli-kick (2PK) protocol with temporal sampling, we demonstrate this mechanism in a fixed-magnetization sector of deterministic XXZ spin chains with a single integrability-breaking bulk defect. We derive an analytical selection rule for the Pauli kicks and show that symmetry-preserving strings with a specific domain-wall count, fixed by the couplings, govern design formation. An exhaustive search over all admissible Pauli strings identifies a broad family of kicks that produce designs in the chaotic regime, whereas no such kicks exist in the integrable limit, including for boundary defects. We further show that the design-forming mechanism remains effective for weak bulk defects as the system size increases.