The numerical solution of the many-body problem, which involves interacting electrons and ions, is a key challenge in condensed matter physics, chemistry, and materials science. Traditional methods to solve the multicomponent quantum Hamiltonian are usually specialized for one kind of particles—electrons or ions—and can suffer from a methodological gap when applied to the other ones. This work extends the self-consistent harmonic approximation, a proven successful technique for simulating quantum ions at finite temperatures in anharmonic crystals, to electrons. The approach minimizes the total free energy by optimizing an ansatz density matrix, solving a fermionic self-consistent harmonic Hamiltonian on a curved manifold parameterized through a neural network. This approach preserves an analytical expression for entropy, enabling the direct computation of free energies and phase diagrams of materials. By benchmarking this technique across several prototypical cases—a double-well potential, the hydrogen atom, and the ${\mathrm{H}}_2$ dissociation—we demonstrate that it can address both the ground- and excited-state properties of electronic systems, capture quantum tunneling and static electronic correlations, and thereby provide a unified quantum framework of electrons and atomic nuclei.

We investigate the thermoelectric properties of a one-dimensional quantum system in the presence of an external driving. We employ Floquet scattering theory to calculate linear-response stationary thermoelectric figures of merit in a single-channel conductor subjected to a periodically varying deltalike potential barrier. We also include a step barrier in one of the leads as a model of a nanoscale inhomogeneous semiconducting system. In the absence of a step barrier, we found that external driving can significantly enhance the Seebeck coefficient, particularly at low temperatures, with a relative increase of up to 200% at high frequencies compared to the static case. In the presence of a step barrier, we found that the thermoelectric Onsager coefficient for the driven case is also enhanced compared to the static case, with a significant photon-assisted effect at low temperatures when the chemical potential is within the semiconductor's gap. Our results demonstrate that external driving can be used to tune and enhance the thermoelectric capabilities of low-electron-density nanodevices.

We report an experimental approach to excite, stabilize, and continuously track Bloch sphere trajectories of dipolar-coupled nuclear spins in a solid. We demonstrate these capabilities on a model system of hyperpolarized ${}^{13}\mathrm{C}$ nuclear spins in diamond. We elucidate a method to drive, and preserve, the motion of spins in complex three-dimensional trajectories for over $T_2^{\prime }>27\mathrm{s}$ even in the presence of interspin coupling. Indeed, without quantum control, interspin interactions lead to rapid spin decay in $T_2^{*}\approx 1.5\mathrm{ms}$. Furthermore, we show that the motion of the spins can be continuously tracked in three dimensions on the Bloch sphere for over $35\mathrm{s}$. During this time the spins complete $>68000$ closed precession orbits, exhibiting high stability and robustness against error. Leveraging these long-lived, robust spin trajectories we devise a novel nonequilibrium quantum sensing scheme for DC magnetic fields, based on micromotion dynamics, and without a static counterpart. Sensing here proceeds for the entire $T_2^{\prime }$ period, orders of magnitude longer than $T_2^{*}$, and operates in the dense sensor limit, yielding significant sensitivity improvements. Our results suggest new ways to stabilize and interrogate strongly coupled quantum systems through periodic driving and portend powerful applications of rigid spin orbits in quantum sensing.

Photoexcited ${\mathrm{K}}_3{\mathrm{C}}_{60}$ displays several properties reminiscent of equilibrium superconductivity, including transient optical spectra, pressure dependence, and $I$–$V$ characteristics. However, these observations do not decisively establish nonequilibrium superconductivity, which may be further evidenced by transient magnetic field expulsion measurements, as shown recently in driven $\mathrm{YB}{\mathrm{a}}_2\mathrm{C}{\mathrm{u}}_3{\mathrm{O}}_{6.48}$. Here, we search for transient magnetic field expulsion in ${\mathrm{K}}_3{\mathrm{C}}_{60}$ by measuring Faraday rotation in a magneto-optic material placed in its vicinity. Unlike in the case of $\mathrm{YB}{\mathrm{a}}_2\mathrm{C}{\mathrm{u}}_3{\mathrm{O}}_{6.48}$, inhomogeneous, metallic ${\mathrm{K}}_3{\mathrm{C}}_{60}$ powders reduce the size of the effect. With the ∼50 nT magnetic field resolution achieved in our experiments, we provide an upper limit for the photoinduced diamagnetic volume susceptibility (${\chi }_v>-0.1$). On this basis, we conclude that the photoinduced phase has weaker magnetic susceptibility than superconducting ${\mathrm{K}}_3{\mathrm{C}}_{60}$ at zero temperature. Yet, from recent nonlinear transport measurements in this granular material, we expect a light-induced state similar to the equilibrium superconductor near $0.8T_c$, for which ${\chi }_v>-0.1$. A definitive conclusion on the presence or absence of Meissner diamagnetism cannot be made for ${\mathrm{K}}_3{\mathrm{C}}_{60}$ with the current resolution.

Exceptional points (EPs) in anti-parity-time (APT)-symmetric systems have attracted significant interest. While linear APT-symmetric systems exhibit structural similarities with nonlinear dissipative systems, such as mutually injection-locked lasers, the correspondence between exceptional points in linear non-Hermitian Hamiltonians and bifurcation phenomena in nonlinear lasing dynamics has remained unclear. We demonstrated that, in a two-cavity system with APT symmetry and gain saturation nonlinearity, an EP coincides with a bifurcation point of nonlinear equilibrium states, which appears exactly at the lasing threshold. Although the EP and the bifurcation point originate from fundamentally different physical concepts, the bifurcation point is observable and retains key EP characteristics even above the lasing threshold. Notably, the bifurcation point that originates from the linear EP also bridges linear and nonlinear dynamics of the system: It serves as an accessible transition point in the nonlinear dynamics between the limit cycle and synchronization regimes. Furthermore, we clarified that beat oscillation that conserves the energy difference, which is a unique dynamic in the weak-coupling regime of a linear APT system, evolves into a nonlinear limit cycle with equal amplitudes in the two cavities in the presence of gain saturation. Our findings establish a direct link between EP-induced bifurcation points and nonlinear dynamics, providing fundamental insights into non-Hermitian and nonlinear optical systems.

Valleytronics, as an alternative to traditional electronics or spintronics, is based on the encoding of quantum information in pseudospin valley quantum numbers, rather than in charge or spin states. A key ingredient is the (optical) manipulation of valley states before loss of coherence, which can be as fast as 100 fs. Previous works have shown the possibility of valley state manipulation using external fields. Here, we propose uniaxial strain as a more flexible and robust scheme to manipulate the valley state through the breaking of the crystal symmetry and the concomitant lifting of the degeneracy of the $1s$ exciton energy. Our theory is corroborated by state-of-the-art numerical simulations in monolayer hBN and shows the possibility to control valley pseudospin at the attosecond timescale.

Bismuth has been shown to be topological in its different allotropes and compounds, with one of the most notable examples being the Bi-Sb alloy, the first 3D topological insulator ever discovered. In this paper, we explore two-dimensional alloys of Bi and Sb, both crystalline and amorphous, to determine the critical concentrations that render the alloys topological. For the amorphous alloy, we determine the effect of structural disorder on its topological properties, remarkably observing a trivial to topological transition as disorder increases. The alloys are modeled using a Slater-Koster tight-binding model and the topological behavior is assessed through the entanglement spectrum together with artificial neural networks. Additionally, we perform electronic transport calculations with results compatible with those of the entanglement spectrum, which, furthermore, reveal an insulator to metal transition in the highly disordered regime.

Ultrahigh nonreciprocal transmission has been achieved in a cavity-magnon system, which consists of two whispering gallery modes (WGMs) and a single magnon mode within a magnetic insulator yttrium iron garnet sphere. The nonreciprocal frequency shift induced by the Sagnac effect enables unidirectional transmission of an input field, while suppressing propagation in the opposite direction, thereby facilitating nonreciprocal optical transmission. Within experimentally accessible parameter regimes, the optical isolation ratio can exceed 40 dB, representing the highest isolation ratio reported to date. Furthermore, applying squeezing to the magnon mode further enhances this isolation performance. Additionally, the directionality of light isolation can be reversed simply by modifying the rotation of the WGM cavity. These findings offer promising prospects for developing high-performance, tunable, and compact optical nonreciprocal devices.

Partition function zeros are powerful tools in understanding critical behavior. In this paper, we present results of the Fisher zeros of two-dimensional Ising models, in the framework of free-fermion eight-vertex model. First, we succeed in finding special boundary conditions for the free-fermion model, under which the partition function of a finite lattice can be expressed in a double product form. Using appropriate mappings, these boundary conditions are transformed into the corresponding versions of the square, triangular, and honeycomb lattice Ising models. Each Ising model is studied in the cases of a zero field and of an imaginary field $i(\pi /2)k_{B}T$. For the square lattice model, we rediscover the famous Brascamp-Kunz (B-K) boundary conditions. For the triangular and honeycomb lattice models, we obtain the B-K-type boundary conditions, and the Fisher zeros are conveniently solved from the product form of partition function. The advantage of B-K-type boundary conditions is that the Fisher zeros of any finite lattice exactly lie on certain loci, and the accumulation points of zeros can be easily determined in the thermodynamic limit. Our finding and method would be very helpful in studying the partition function zeros of vertex and Ising models.

Numerous experiments have shown that $\alpha \text{−}\mathrm{RuC}{\mathrm{l}}_3$ exhibits a spin liquid (SL) state near 7.1 T when an in-plane magnetic field is applied perpendicular to the Ru-Ru bond directions ([110]), while SL states are rarely observed under fields applied along the Ru-Ru bond ([100]). The underlying mechanism for this pronounced anisotropy remains elusive. In this work, we employ semiclassical spin dynamics simulations to investigate the magnetization evolution of $\alpha \text{−}\mathrm{RuC}{\mathrm{l}}_3$ with lattice distortion under varying external magnetic fields. It is found that each [100] direction has its own dominant orientation, and each [110] orientation marks the boundary, where the two alignments compete with each other. The magnetizations are influenced by multiple interactions and perturbations from lattice distortions, leading to the occurrence of the SL state in the [110] direction. These results provide new insights into the field-induced phase transitions in $\alpha \text{−}\mathrm{RuC}{\mathrm{l}}_3$ and the microscopic mechanisms underlying the emergence of spin liquid behavior.

The nontrivial integration of qubits with classical computing systems and the lack of quantum-memory devices remain a key obstacle in the development of quantum technologies. Here, we present a theoretical platform for hybrid quantum devices with memory characteristics. In these current-driven hybrid memristors, a ferroelectric layer serves as the tunneling barrier in a superconducting Josephson junction; thus, the potential barrier is history-dependent. A memory-integrated phase qubit and a Lagrangian description of the superconducting circuit are also presented, paving the way to highly functional, self-modulated Josephson-junction technologies.

Phase separation routinely occurs in both living and synthetic systems. These phases are often complex and distinguished by features including crystallinity, nematic order, and a host of other nonconserved order parameters. For systems at equilibrium, the phase boundaries that characterize these transitions can be straightforwardly determined through the framework of thermodynamics. The prevalence of phase separation in active and driven systems motivates the need for a genuinely nonequilibrium theory for the coexistence of complex phases. Here, we develop a dynamical theory of coexistence when both conserved and nonconserved order parameters are present, casting coexistence criteria into the familiar form of equality of state functions. Our theory generalizes thermodynamic notions such as the chemical potential and Gibbs-Duhem relation to systems out of equilibrium. While these notions may not exist for all nonequilibrium systems, we numerically verify their existence for a variety of systems by introducing phenomenological active field theories. We hope our work aids in the development of a comprehensive theory of high-dimensional nonequilibrium phase diagrams.

The early prediction of tipping points, distinguished by sudden and catastrophic shifts from stable states, poses a challenging task that would enable us to assess the impending threat across natural and engineered systems. This threat becomes particularly acute in low-fluctuation environments, where tipping occurs through saddle-node bifurcation without prior warning in noise dynamics. In this study, we investigate the tipping point dynamics of avalanche catastrophes in low-fluctuation domain, employing model system like the zero-temperature random-field Ising model and thermally deposited cobalt films. As the system approaches the tipping point, avalanche activity reveals pronounced critical behavior, including critical slowing-down, variance enhancement, and a growing spatial correlation length—hallmarks that may serve as early warning signals of impending collapse. Crucially, we demonstrate that increasing disorder in the system reduces its vulnerability to catastrophic failure. In highly disorder regimes, these early warning signals emerge well before the transition, thereby providing a large margin for anticipation and mitigation. This key finding suggests a protective role of disorder offering a perspective on resilience in complex systems. Our results not only deepen the understanding of tipping phenomena in disorder materials but also have broader implications for forecasting regime shift in diverse real-world systems.

We propose and demonstrate a method to manipulate x-ray emission rates and directions by coupling them to surface plasmon polaritons via x-ray-to-ultraviolet down-conversion in a metal. This mechanism generates highly correlated photon pairs, each consisting of one x-ray and one ultraviolet photon, enabling fine control of x-ray angular and spectral characteristics through the ultraviolet photons resonant with the surface plasmons. Our approach bridges a previously insurmountable gap between x-ray and plasmonic energy and momentum, enabling the use of engineered plasmonic structures to control x-ray emission. Furthermore, our work unlocks opportunities to explore plasmonic physics at the microscopic scale with atomic-scale resolution.

The local magnetic anisotropy of a typical crystalline compound is usually attributed to the combined effect of crystal electric fields and spin-orbit coupling. We show that this simple local picture is transformed in heavy-fermion compounds by the development of coherent electron scattering from local spin degrees of freedom. Provided the dominance of the coherence energy scale over the magnetic energy scale is strong enough, the fractionalization and delocalization of the spins destabilizes their single-ion anisotropy by generating an opposing anisotropy in the exchange. Experimentally, this can manifest as competing splittings in the Curie-Weiss constants and effective moments. We show that in the presence of orthorhombic or tetragonal symmetry, the destabilization of the anisotropy can result in either ferromagnetic or antiferromagnetic order that is perpendicular to the high-temperature easy axis. In the absence of destabilization, we show that the order is more likely to be antiferromagnetic. In agreement with our theory, we also observe that the temperature at which the anisotropy of the uniform magnetic response changes tracks the coherence energy scale in a wide range of actinide and lanthanide compounds.