We present single-crystal neutron diffraction, powder muon spin rotation, and pulsed-field magnetometry measurements on the Heisenberg quantum chiral chain $\left[\mathrm{Cu}\left(\mathrm{pym}\right){\left({\mathrm{H}}_2\mathrm{O}\right)}_4\right]{\mathrm{SiF}}_6·{\mathrm{H}}_2\mathrm{O}$ (pym = pyrimidine), which displays a fourfold-periodic rotation of the local environment around the Cu(ii) $S=1/2$ ions from site to site along the chain. Previous measurements on this material have shown the absence of magnetic order down to surprisingly low temperatures $\ge 20$ mK, as well as the presence of an energy gap for magnetic excitations that grows linearly with magnetic field. Here we find evidence at dilution refrigerator temperatures for a field-induced transition to long-range magnetic order above an applied magnetic field of 3 T. From the polarization of magnetic moments observed with magnetic fields applied in the $[-1,2,0]$ direction, we can identify the static magnetic structure that best accounts for the data. The proposed model is supported microscopically by the presence of an alternating component of the $g$ tensor, which produces an internal twofold staggered field that dictates both the direction of the ordered moments and the effective coupling between adjacent chains. The observed magnetic structure is contrary to previous proposals for the departure of the magnitude and field dependence of the energy gap from the predictions of the sine-Gordon model.

Nonstoichiometric Mn-substituted $\mathrm{ErF}{\mathrm{e}}_2$ compounds, historically and hereafter written as $\mathrm{ErF}{\mathrm{e}}_2\mathrm{M}{\mathrm{n}}_x$ ($x=0-0.4$), with the $\mathrm{MgC}{\mathrm{u}}_2$-type cubic Laves-phase structure, magnetically ordered at room temperature, have been probed by ${}^{57}\mathrm{Fe}$ Mössbauer spectroscopy, aiming at the determination of the influence of Mn atoms on the state of iron and clarification of Mn atomic distribution in the lattice. Mössbauer spectra have been processed in the frame of the tensor approach to the description of hyperfine interactions, which allowed determination of the main hyperfine parameters and partition of the isotropic and anisotropic parts of the hyperfine field at Fe nuclei, with its direction being set down. The magnetic moment at Fe atoms at room temperature is estimated to be $1.3{\mu }_{\mathrm{B}}$ for $\mathrm{ErF}{\mathrm{e}}_2$ and it decreases with increasing the Mn content. The magnetic moments of Fe and Mn are ordered ferromagnetically, with Mn atoms having a lower magnetic moment than Fe. The direction of the hyperfine field at ${}^{57}\mathrm{Fe}$ lies in the plane (1-10) and deviates from the [111] axis. The deviation angle increases with increasing Mn concentration. It is shown that the distribution of Mn in the structure of $\mathrm{ErF}{\mathrm{e}}_2\mathrm{M}{\mathrm{n}}_x$ differs from the statistical one, which purports its local ordering. A strong impact of Mn that occupies sites in the rare-earth sublattice on Fe atoms is observed, unlike earlier Mössbauer experiments on quasibinary compounds with the structure of the cubic Laves phase.

First-principles-based effective Hamiltonian techniques have been widely employed for over three decades to investigate ferroelectricity and related phenomena in perovskite materials. These techniques offer high accuracy, transferability, compatibility with various finite-temperature algorithms, computational efficiency, and ease in incorporating interactions with external fields. They have been adapted to study diverse phenomena, ranging from topological dipole patterns in ferroelectric nanostructures to multicaloric effects. In this work, we develop an effective Hamiltonian for the nonperovskite ferroelectric ${\mathrm{HfO}}_2$ (hafnia). Applying this methodology to explore the finite-temperature and finite-electric-field properties of ferroelectric hafnia revealed (1) exceptionally large intrinsic coercive fields, an order of magnitude higher than those observed in perovskite ferroelectrics; (2) their atomistic origin; and (3) the existence of a regime where the relationship between the coercive field and the energy barrier for polarization reversal is counterintuitive. These developments could accelerate progress both in methodological advancements for simulating ferroics and in the atomistic understanding of a broad range of ferroelectrics.

We build and discuss a low energy effective field theory for anisotropic antiferromagnets in the presence of an external magnetic field. Such an effective theory is simple yet rich and features a number of phenomena such as the appearance of gapped Goldstones, pseudo-Goldstones, and a first order “spin flop” phase transition, all within the regime of validity of the theory. We also discuss in detail, the quantization procedure of the free theory in the presence of a magnetic field, which is made nontrivial by the presence of a single-time derivative term. This class of materials makes a precious test field for exotic phenomena in quantum field theory. Moreover, we explicitly perform the matching of the effective theory to the short distance theory of a specific antiferromagnet, namely, nickel oxide. The latter is particularly relevant in light of recent proposals of employing this material towards the hunt for light dark matter. As a byproduct of our study, we also re-evaluate the role played by discrete symmetries in magnetic materials, presenting it in a way that is completely consistent with the proper low energy EFT ideology.

A promising path to realizing higher superconducting transition temperatures $T_{\mathrm{c}}$ is the strategic engineering of artificial heterostructures. For example, quantum materials could, in principle, be coupled with other materials to produce a more robust superconducting state. In this work, we add numerical support to the hypothesis that a strongly interacting superconductor weakened by phase fluctuations can boost its $T_{\mathrm{c}}$ by hybridizing the system with a metal. Using determinant quantum Monte Carlo, we simulate a two-dimensional bilayer composed of an attractive Hubbard model and a metallic layer in two regimes of the interaction strength $-\left|U\right|$. In the strongly interacting regime, we find that increasing the interlayer hybridization $t_{\perp }$ results in a nonmonotonic enhancement of $T_{\mathrm{c}}$, with an optimal value comparable to the maximum $T_{\mathrm{c}}$ observed in the single-layer attractive Hubbard model, confirming trends inferred from other approaches. In the intermediate coupling regime, when $-\left|U\right|$ is close to the value associated with the maximum $T_{\mathrm{c}}$ of the single-layer model, increasing $t_{\perp }$ tends to decrease $T_{\mathrm{c}}$, implying that the correlated layer was already optimally tuned. Importantly, we demonstrate that the mechanism behind these trends is related to enhancement in the superfluid stiffness, as was initially proposed by Kivelson [Phys. B: Condens. Matter 318, 61 (2002)].

We investigate in detail the $\nu =+1$ displacement-field-tuned interacting phase diagram of $L=3,4,5,6,7$ layer rhombohedral graphene aligned to hBN ($\mathrm{R}L\mathrm{G}$/hBN). Our calculations account for the 3D nature of the Coulomb interaction, the inequivalent stacking orientations $\xi =0,1$, the effects of the filled valence bands, and the choice of “interaction scheme” for specifying the many-body Hamiltonian. We show that the latter has a dramatic impact on the Hartree-Fock phase boundaries and the properties of the phases, including for pentalayers (R5G/hBN) with large displacement field $D$, where recent experiments observed a Chern insulator at $\nu =+1$ and fractional Chern insulators for $\nu <1$. In this large $D$ regime, the low-energy conduction bands are polarized away from the aligned hBN layer, making them well described by the folded bands of moiréless rhombohedral graphene at the noninteracting level. Despite this, the filled valence bands develop moiré-periodic charge density variations, which can generate an effective moiré potential, thereby explicitly breaking the approximate continuous translation symmetry in the conduction bands and leading to contrasting electronic topology in the ground state for the two stacking arrangements. Within time-dependent Hartree-Fock theory, we further characterize the strength of the moiré pinning potential in the Chern insulator phase by computing the low-energy $\mathbf{q}=0$ collective mode spectrum, where we identify competing gapped pseudophonon and valley magnon excitations. Our results emphasize the importance of careful examination of both the single-particle and interaction model for a proper understanding of the correlated phases in $\mathrm{R}L\mathrm{G}$/hBN.

The fractional Chern insulators (FCIs) observed in pentalayer rhombohedral graphene/hexagonal boron nitride superlattices have a unique origin contrary to theoretical expectations: their noninteracting band structure is gapless, unlike standard FCIs and the Landau level. Hartree-Fock (HF) calculations at filling $\nu =1$ yield a gapped ground state with Chern number 1 through band mixing, identifying a possible parent state. However, many-body calculations restricted to the occupied HF band predispose the system toward FCIs and are essentially uncontrolled. In this work, we use unbiased multiband exact diagonalization (ED) to allow fluctuations into the gapless bands for two normal-ordering schemes. In the “charge neutrality” scheme, the weak moiré potential leads to theoretical proposals based on Wigner crystal-like states. However, we find that FCIs seen in one-band ED calculations are destroyed by band mixing, becoming gapless as fluctuations are included. In the “average” scheme, the Coulomb interaction with the periodic valence charge background sets up a stronger moiré potential. On small systems, FCIs at $\nu =1/3$ are destroyed in multiband calculations, while those at $\nu =2/3$ are initially strengthened. However, we do not converge to a stable FCI at $\nu =2/3$ even on the largest accessible systems. These findings question prior results obtained within projection to a single HF band. They suggest that current models do not support FCIs with correlation length small enough to be converged in current unbiased ED calculations, or do not support FCIs at all.

Majorana zero modes (MZMs) at the boundary of topological superconductors (TSC) have garnered significant attention for their application in quantum computation. In this study, we demonstrate that in heterostructures composed of the one-dimensional (1D) chiral nanowire and a superconductor, structural chirality could induce the spin-triplet-polarized MZMs. Interestingly, the opposite spin-polarized MZMs are robustly localized at the end of nanowire, whose direction depends on the chirality. Furthermore, this spin-triplet polarization gives rise to chirality-dependent spin-polarized local Andreev reflection (LAR) processes at the TSC/normal metal interface, providing a mechanism for detecting MZMs in TSC-based devices. Finally, we also demonstrate that the chirality-dependent spin-polarized MZMs and LAR processes could be realized in the experimentally accessible 1D helical ${\mathrm{NbSe}}_{\text{3}}$ nanowire. Thus, our findings offer insights into the realization and manipulation of MZMs in 1D chiral systems, with implications for spintronic applications in TSC-based devices.

The importance of simple geometrical invariants, such as the Berry curvature and quantum metric, constructed from the Bloch states of a crystal has become well established over four decades of research. More complex aspects of geometry emerge in properties linking multiple bands, such as optical responses. In the companion work [Phys. Rev. Lett. 135, 066901 (2025)], we introduced multistate geometrical invariants using an explicitly gauge-invariant formalism based on projection operators, which we used to clarify the relation between the shift current and the theory of electronic polarization among other advancements for second-order nonlinear optics. Here, we provide considerably more detail on the projector formalism and the geometrical invariants arising in the vicinity of a specific value of crystal momentum. We combine the introduction to multistate quantum geometry with broadly relevant algebraic relationships and detailed example calculations, enabling extensions toward future applications to topological and geometrical properties of insulators and metals.

We investigate the emergence of topological features in the charge excitations of Mott insulators in the Chern-Hubbard model. In the strong correlation regime, treating electrons as the sum of holons and doublons excitation, we compute the topological phase diagram of Mott insulators at half-filling using composite operator formalism. The Green's function zeros manifest as tightly bound pairs of such elementary excitations of Mott insulators. Our analysis examines the winding number associated with the occupied Hubbard bands and the band of Green's function zeros. We show that both the poles and zeros exhibit gapless states and zeros, respectively, in line with bulk-boundary correspondence. The gapless edge states emerge in a junction geometry connecting a topological Mott band insulator and a topological Mott zeros phase. These include an edge electronic state that carries a charge and a charge-neutral gapless zero mode. Our study is relevant to several twisted materials with flat bands where interactions play a dominant role.

The formulation of descriptors of the local chemical environment, enabling the construction of machine-learning models, is usually obtained by studying the properties of the expansion coefficients of a neighborhood density. In this work, we show that all the transformation properties of the descriptors and their behavior under rotation, inversion, and complex conjugation are derived from the choice of the basis over which the density is expanded. Furthermore, crucially, they are independent from the explicit mathematical form of the neighborhood density. In particular, we show that all the descriptors investigated can be obtained by an expansion in multipolar spherical harmonics, which constitutes the core of this work, and which is introduced and analyzed in great detail. By exploiting the orthogonality and the transformation rules of the multipolar spherical harmonics, we show that several formulations are simplified, such as the one needed to obtain the $\lambda \text{−}\mathrm{SOAP}$ kernel and its properties. We close this work by applying our framework to several multibody descriptors available in literature, providing an in-depth analysis of their main properties, as made clear from the vantage viewpoint of a basis-centered approach.

We calculate the shift current response in twisted double bilayer graphenes (TDBG) by applying the perturbative approach to the effective continuum Hamiltonian. We have performed a systematic study of the shift current in AB-AB and AB-BA stacked TDBG, where we have investigated the dependence of the signal on the twist angle, vertical bias voltage, and Fermi level. The numerical analyses demonstrate that the signal is greatly enhanced as the twist angle is reduced. Notably, we also found that there is a systematic sign reversal of the signal in the two stacking configurations below the charge neutrality point for large bias voltages. We qualitatively explain the origin of this sign reversal by studying the shift current response in AB-stacked bilayer graphene.

Proposed as an elegant symmetry relating bosons and fermions, spacetime supersymmetry (SUSY) has been actively pursued in both particle physics and emergent phenomena in quantum critical points (QCPs) of topological quantum materials. However, how SUSY casts the light on nonequilibrium dynamics remains open. In this Letter, we investigate the Kibble-Zurek dynamics across a QCP with emergent $\mathcal{N}=2$ spacetime SUSY between the Dirac semimetal and a superconductor through a large-scale quantum Monte Carlo simulation. The scaling behaviors in the whole driven process are uncovered to satisfy the full finite-time scaling (FTS) forms. More crucially, we demonstrate that the emergent SUSY manifests in the intimate relation between the FTS behaviors of fermionic and bosonic observables, namely the fermions and bosons acquire identical anomalous dimensions. Our work not only brings a fundamental ingredient into the critical theory with SUSY, but also provides the theoretical guidance to experimentally detect QCPs with emergent SUSY from the perspectives of the Kibble-Zurek mechanism and FTS.

We calculate the full counting statistics of charge transfer in a chiral Majorana interferometer—a setup where a Dirac mode (an electron-hole mode) is split into two Majorana modes that encircle a number of $h/2e$ vortices in a topological superconductor. Without any coupling to the environment it is known that the low-energy charge transfer is deterministic: an electron is transferred either as an electron or as a hole, dependent on the parity of the vortex number. We show that a stochastic contribution appears if which-path information leaks into the environment, producing the shot noise of random $2e$ charge transfers with binomial statistics. The Fano factor (dimensionless ratio of shot noise power and conductance) increases without bound as the which-path detection probability tends to unity.

Giant impacts in the final stage of planet formation could induce partial melting and vaporization of colliding bodies. However, the critical conditions required for the vaporization of constituent materials as well as the fraction of material that undergoes vaporization during such impacts remain uncertain. In this work, we present the shock equation of state and critical vaporization of $\mathrm{MgSi}{\mathrm{O}}_3$, the most abundant mineral in the lower mantle, using first-principles molecular dynamics. The critical point of $\mathrm{MgSi}{\mathrm{O}}_3$ is determined to be 7093 ± 41 K and 0.73 ± 0.05 $\mathrm{g}\mathrm{c}{\mathrm{m}}^{-3}$. The behavior of the Hugoniot curve is investigated under different initial conditions. We find that the critical shock pressure required to vaporize $\mathrm{MgSi}{\mathrm{O}}_3$ under ambient conditions is 253 ± 27 GPa, whereas a warm initial state of 1 GPa and 1500 K reduces this value to 152 ± 8 GPa. The corresponding impact velocities necessary to achieve vaporization are estimated to be 9.3 $\mathrm{km}{\mathrm{s}}^{-1}$ for an iron projectile and 11.8 $\mathrm{km}{\mathrm{s}}^{-1}$ for a forsterite projectile under ambient conditions and reduce to 7.3 and 9.1 $\mathrm{km}{\mathrm{s}}^{-1}$, respectively, under the warm initial state. Our findings indicate that giant impacts could vaporize a substantial portion of mantle materials, thereby facilitating compositional mixing and chemical equilibration within the mantle.

It is well documented that the solid-state phase transition types are generally controlled by kinetic conditions (e.g., cooling/heating rate) and thermodynamic factors (e.g., temperature). Applying in situ transmission electron microscopy as well as theoretical calculations and simulations, we unexpectedly discover two competing transition types of β-phase single-crystalline tungsten nanoparticles (NPs) that are mediated by size and impurity. Under thermal heating, a nonclassical diffusion-mediated fast transition from β to α phase is identified in NPs with sizes >100 nm. Concerning the NPs with sizes <100 nm, we detect a distinct interface-controlled diffusion mechanism, driving the β to hexagonal close-packed (hcp) phase transition with much slower transition rate. By investigating the overall energy landscape of the α, β, and hcp phases as a function of both size and light element impurity (hydrogen and oxygen), we uncover the possible origin of two different transition modes. Our observations highlight the complex interplay of various parameters in mediating the solid-phase transition modes, and thus offer in-depth insights into designing the functionalized low-dimensional materials.

Quasiperiodic models are important physical platforms to explore Anderson transitions in low dimensional systems, yet the exact mobility edges (MEs) are generally hard to be determined analytically. To date, the MEs in only a few models can be determined exactly. In this manuscript, we propose a class of network models characterized by quasiperiodic slowly varying potentials and the absence of hidden self-duality and exactly determine their MEs. We take the mosaic models with slowly varying potentials as examples to illustrate this result and derive its MEs from the effective Hamiltonian. In this method, we can integrate out the periodic sites to obtain an effective Hamiltonian with energy-dependent potentials $g\left(E\right)V$ and effective eigenenergy $f\left(E\right)$, which directly yields the MEs at $f\left(E\right)=\pm [2t^{\kappa }\pm g\left(E\right)V]$, where $\kappa \in {\mathbb{Z}}^{+}$. With this idea in hand, we then generalize our method to more quasiperiodic network models, including those with much more complicated geometries and non-Hermitian features. Finally, we propose the realization of these models using optical waveguides and show that the Anderson transition can be observed even in small physical systems (with lattice sites about $L=50–100$). Our results provide some key insights into the understanding and realization of exact MEs in experiments.

In this work, we demonstrate the coexistence of reentrant localization and dynamical delocalization in a one-dimensional non-Hermitian quasiperiodic lattice. Specifically, by considering a nonreciprocal dimerized lattice, we show that the additional off-diagonal quasiperiodic disorder can drive the system through two localization transitions as the disorder strength increases, a phenomenon that is absent in the corresponding reciprocal model. In this process, certain initially localized states are transformed back into extended states, leading to the emergence of a second critical region that holds the single-particle mobility edge. Interestingly, our investigation of the wave-packet dynamics reveals that within a part of the first initially localized region and the whole second localized region in the reentrant localization, the wave packet exhibits spatial spreading, also known as dynamical delocalization. This highly unusual behavior stems from the imaginary part (finite lifetime) of localized states during localization transitions. We validate these observations by analyzing participation ratios, the single-particle spectrum, finite-size analysis, and wave-packet evolution, culminating in a phase diagram that clearly delineates the phase transitions. Our work further enriches the understanding of reentrant localization phenomena and the associated wave-packet dynamics in quasiperiodic systems.

Discrete time crystals (DTCs) are a nonequilibrium phase of matter characterized by the breaking of time-translation symmetry in periodically driven quantum systems. In this work, we present a detailed thermodynamic analysis of a DTC in a one-dimensional spin-1/2 chain coupled to a thermal bath. We derive a master equation from the microscopic model, and we explore key thermodynamic quantities, such as work, heat, and entropy production. Our results reveal that the DTC signature inevitably decays in the presence of environmental noise, but we show that a periodic measurement scheme can mitigate the effects of decoherence, stabilizing the subharmonic oscillations of the DTC for extended periods. These findings provide insights into the robustness of time-crystalline phases and potential strategies for protecting them in experimental settings.