We propose a methodology to generate hybrid machine learning models for the potential energy surface trained simultaneously on data from ab initio electronic structure calculations and on thermodynamic and/or structural observables from experiment. The approach is based on the use of a loss function that includes the mean square error of observables with respect to their experimental values, in addition to the usual terms involving the mean square error of the energies and forces with respect to ab initio data. We employ a reweighting procedure that allows for the calculation of ensemble averages of observables during training for arbitrary values of the model parameters and on the fly. The method is general and can be applied to any set of static observables. We illustrate the usefulness of this approach by applying it to the generation of hybrid models for water that reproduce accurately the experimental density maximum and the radial distribution function of liquid water in molecular dynamics simulations.

We reveal a mechanism that may explain the nonmetallic out-of-plane resistivity in layered metals. By carefully examining how the Drude-Boltzmann expression for the $c$-axis conductivity emerges out of the Kubo formula, we find, besides the standard metallic term proportional to the carrier lifetime $\tau$, a non-Drude contribution proportional to $1/\tau$. The Drude behavior breaks down when $1/\tau >2{\eta }^{*}$, the crossover value ${\eta }^{*}$ being small (and hence observable) when the $c$-axis velocities vary rapidly with the distance from the Fermi surface. We consider the Hund metal ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ as a test case, which we study within a realistic dynamical mean-field theory approach. The non-Drude behavior observed experimentally in $c$-axis transport is reproduced and explained by our considerations, showing that earlier invoked extrinsic mechanisms that involve either impurities or phonons are unnecessary. Although the small value of ${\eta }^{*}$ arises from a peculiar accidental cancellation due to destructive interference, characteristic of body-centered tetragonal lattices, we emphasize and discuss the generality of this mechanism.

A widespread experimental realization of quantized anomalous transport in the intrinsic magnetic topological insulator ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ is hindered by its elusive surface magnetic gap. Uncovering the origin of the gapless states is thus essential for accessing its topological properties. Here, we show that surface defects lower the electrostatic potential, drive topological surface states into subsurface layers, and suppress exchange interactions, thereby closing the gap. Tuning the surface electrostatic potential via external electric fields or interfacial fields in van der Waals heterostructures restores the expected gap and enables control of its topology. This is confirmed by model calculations and validated in defective ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ films interfaced with polar insulators, explaining the enhanced quantum anomalous Hall effect under ${\mathrm{AlO}}_x$ capping observed in recent experiments. Our theory identifies electrostatically driven surface-state delocalization as a competitive origin of gap suppression and proposes displacement-field engineering for robust quantized transport.

Understanding charge transport in strongly correlated systems remains a central challenge in condensed matter physics, while exact analytical results for finite-temperature transport remain rare. Here, we investigate charge transport in the one-dimensional Hubbard model in the infinite-interaction limit. We first construct the exact and explicit, i.e., beyond Bethe ansatz energy spectrum and eigenstates. Building on these explicit eigenstates, we derive a closed-form analytical expression for the charge Drude weight at arbitrary temperatures in the hole-dilute limit with a fixed number of doped holes, as well as analytical expressions in the low- and high-temperature limits at fixed hole density. We further show that, at low temperatures, the leading correction to the charge Drude weight is linear in $T$ when the number of holes is fixed, whereas it is quadratic in $T$ when the hole density is fixed. This analytically controlled example highlights the importance of identifying the underlying thermodynamic trajectory when interpreting finite-size numerical studies of charge transport in more general models.

The nature of the charge density wave (CDW) order of the rare-earth tritelluride ${\mathrm{ErTe}}_3$ is investigated by Raman scattering under anisotropic strain. The CDW state of ${\mathrm{ErTe}}_3$ is unconventional since it is accompanied by an unusual mirror symmetry breaking, whose origin remains to be understood. Studying the polarization-resolved Raman spectrum of the CDW amplitude mode as a function of strain and temperature, we find that the mirror symmetry breakings of the CDW state are not independent, arguing against the recently proposed ferroaxial multicomponent CDW order. Instead, we show that a single component CDW order parameter with an ordering wave vector tilted away from the principle crystallographic axis can reproduce the observed mirror symmetry breakings and their manifestation in the Raman spectra.

Quantum geometry is universally bounded from below by Wilson-loop windings. In this Letter, we define an isolated set of bands to be Wilson-loop ideal, if their quantum metric saturates the Wilson-loop lower bound. The definition naturally incorporates the known Chern-ideal and Euler-ideal bands, and allows us to define other types of ideal bands, such as Kane-Mele ${\mathbb{Z}}_2$-ideal and inversion-fragile-ideal bands. In particular, we find that in the case of zero total Chern number, an isolated Wilson-loop-ideal set of two bands with nonsingular non-Abelian Berry curvature and nontrivial normal Wilson-loop winding always admits a Chern-ideal gauge, without the need of a global good quantum number (such as spin). This enables the direct construction of new topologically ordered states, such as fractional topological insulator wave functions. We further propose a general framework of constructing monotonic flows that achieve Wilson-loop-ideal states starting from nonideal bands through band mixing, where Wilson-loop-ideal states are not energy eigenstates but have smooth projectors similar to isolated bands. We apply the constructed flows to the realistic model of 3.89° twisted bilayer ${\mathrm{MoTe}}_2$, a moiré Rashba model, and another moiré time-reversal-breaking model, and numerically find Chern-ideal, ${\mathbb{Z}}_2$-ideal, and inversion-fragile states, respectively, with relative error in the integrated quantum metric below $5\times {10}^{-3}$. Our exact-diagonalization calculations on the numerically ideal states demonstrate the potential of our general definition of Wilson-loop-ideal bands and general procedure of constructing Wilson-loop-ideal states for future study of novel correlated physics.

Reconstructing magnetization textures from nitrogen-vacancy (NV) magnetometry stray-field measurements is a challenging, fundamentally ill-posed inverse problem, further complicated by the unknown effective distance between sensor and magnetic material. Here we show that incorporating a micromagnetic energy functional directly into the inversion filters out unphysical, high-energy configurations, while Fourier-space upward continuation of the stray field allows us to simultaneously fit the distance. Applied to measurements of the van der Waals ferromagnet ${\mathrm{Fe}}_{3-\mathrm{x}}{\text{GaTe}}_2$, it recovers an effective distance estimate of approximately $81\mathrm{n}\mathrm{m}$ and low-energy configurations that reproduce the observed field. More broadly, embedding physics directly into the reconstruction turns ill-posed magnetic inverse problems into transparent, interpretable reconstructions, with applicability well beyond NV magnetometry.

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

Higher-order interactions can induce abrupt collective transitions, yet the microscopic mechanisms controlling macroscopic critical behavior remain unclear. Here we show that nested hyperedges generate a dual effect on dynamical processes: they promote the onset of collective behavior while suppressing the explosive transitions driven by higher-order feedback. To uncover the mechanism, we develop an analytically tractable theory of contagion on hypergraphs that explicitly tracks nestedness between groups of different sizes, allowing us to identify the microscopic mechanism responsible for this dual behavior. By disentangling contagion pathways, we find that nestedness redirects transmission from external links to internal, group-embedded routes—boosting early activation but making dyadic and triadic channels increasingly redundant. This loss of structural independence quenches the nonlinear amplification required for bistability, progressively smoothing the transition as hyperedges become nested. The phenomenology holds for groups of any size and is not specific to spreading dynamics but also emerges in higher-order Ising and Kuramoto dynamics. Overall, our results identify nestedness between group interactions as a general structural mechanism governing critical transitions in complex systems.

Noncommutativity of observables is a defining feature of quantum physics. It plays a fundamental role in the formulation of the uncertainty principle for complementary variables and strongly affects the thermodynamic behavior of systems with noncommuting, that is, non-Abelian, conserved quantities. We here derive extensions of the first and second laws of thermodynamics, including nonequilibrium fluctuation relations, for driven quantum systems. We identify an additional non-Abelian contribution to the energy and entropy balances, without which these relations would be violated. This contribution can be harnessed to enhance both work extraction and nonequilibrium currents compared to what is achieved in commuting thermodynamics. These results demonstrate that noncommutativity is a potentially valuable thermodynamic resource.

We generate multipartite entangled states of two, three, and four matter qubits, where the entanglement is distributed over macroscopic distances via a photonic network link. Trapped-ion ${}^{88}{\mathrm{Sr}}^{+}$ qubits are entangled directly via an optical fibre link, and the entanglement is subsequently extended to ${}^{43}{\mathrm{Ca}}^{+}$ memory qubits cotrapped in each network node, using local mixed-species logic gates. We create remotely entangled ${\mathrm{Sr}}^{+}\text{−}{\mathrm{Ca}}^{+}$ and ${\mathrm{Ca}}^{+}\text{−}{\mathrm{Ca}}^{+}$ states, as well as mixed-species Greenberger-Horne-Zeilinger (GHZ) states of up to four qubits. We demonstrate storage of the remotely entangled memory qubits for $\sim 10\mathrm{s}$, more than $100\times$ the state creation time.

The Landau paradigm has been a powerful framework for understanding phase transitions involving spontaneous symmetry breaking. In contrast, phase transitions between two symmetric phases, where neither phase breaks any symmetry, remain less explored. One intriguing class of such transitions involves “symmetric mass generation” (SMG), where interactions drive a transition from a gapless symmetric phase to a gapped symmetric phase. In this Letter, we develop a controlled perturbative approach to study a class of such transitions, based on an $\epsilon$ expansion around the critical dimension where the SMG-inducing interaction becomes marginal. Applying this method to two distinct models, we identify a single-parameter-tuned transition in each case, which we conjecture captures the universal critical behavior of the SMG transition in these models. We compute universal quantities associated with these transitions.

Quantum frequency conversion (QFC) is essential for bridging the spectral gap between stationary qubits and low-loss optical communication channels. Practicable QFC interfaces connecting ultraviolet and telecommunication bands are of great significance but have remained elusive, constrained by the dual challenges of a high-performance frequency converter and effective noise suppression in short-wavelength pumping configurations. We address this by demonstrating the phase-matching mechanism with domain defects and differential-tuning behavior of the spontaneous parametric down-conversion noises. Based on a quantitative analysis of performance degradation induced by domain defects, we propose specific fabrication guidelines and experimentally achieve an ultrahigh normalized conversion efficiency of $839\%/(\mathrm{W}{\mathrm{cm}}^2)$ for the fundamental guided mode in thin-film lithium niobate waveguides. Meanwhile, we reveal a new noise control mechanism for short-wavelength pumping by utilizing the differential-tuning behaviors of difference-frequency generation and spontaneous parametric down-conversion processes. Then a single-stage QFC from 393 nm to the telecom C band with a record-high external efficiency of 28.8% and an ultralow noise level of 35 counts per second is achieved experimentally. The proposed mechanisms would enable other QFCs with higher efficiency and lower noise, advancing the development of scalable quantum networks. Furthermore, it holds significant potential for driving progress in both classical and integrated nonlinear photonics.

Progress in cavity magnonics relies on tunable nonlinearities in magnon-photon interactions for controlling magnon dynamics and frequency conversion. Here, we demonstrate the magnon Kerr effect in anisotropic magnonic systems comprising iron garnet thin films coupled to a loop-gap microwave resonator. The strong shape anisotropy, combined with strain, enhances the magnon Kerr effect compared to a sphere of equivalent volume by up to 3 orders of magnitude, while the cavity enables sensitive probing of magnetization dynamics. We demonstrate continuous tunability of the magnitude and sign of the Kerr shift by controlling the static orientation of the magnetization, in excellent agreement with theory. Our findings demonstrate a scalable approach to enhancing Kerr anharmonicity in hybrid magnon-photon systems while preserving coherent magnon-photon interactions.

Freely propagating electrons may serve as quantum probes that can become coherently correlated with other quantum systems, offering access to advanced metrological resources. We propose a setup that coherently couples free electrons in an electron microscope to a trapped-ion quantum processor, enabling nondestructive, quantum-coherent detection and the accumulation of information across multiple electrons. Our analysis shows that single electrons can induce resolvable qubit excitations, establishing a platform for practical applications such as quantum-enhanced, dose-efficient electron microscopy.