Rhombohedral boron nitride (rBN), distinguished from its hexagonal counterpart (hBN) by a unique interlayer stacking sequence, has recently garnered considerable attention owing to its unusual optical nonlinearity and interfacial ferroelectricity. However, thermal transport in rBN remains unexplored, despite the critical role for heat dissipation in functional devices. Here, we present a combined experimental and theoretical investigation of heat conduction in bulk rBN. The measured in-plane and out-of-plane thermal conductivities align closely with our first-principles calculations incorporating three-phonon, four-phonon, and phonon-isotope scatterings. Compared to the theoretical thermal conductivities of hBN, about 15% suppression is observed. This is attributed to the lower crystal symmetry and folding of the Brillouin zone induced by the stacking configuration of rBN, which leads to more phonon scattering channels and stronger anharmonicity. In particular, thermal transport via the transverse acoustic phonon modes is primarily impeded. Our work offers a benchmark for the anisotropic thermal conductivity of rBN, and provides insights into phonon transport in commensurate metastable structures of layered materials.

We investigate the thermodynamic properties of the Hubbard model on the Bethe lattice with a coordination number of 3 using the thermal canonical tree tensor network method. Our findings reveal two distinct thermodynamic phases: a low-temperature antiferromagnetic phase, where spin SU(2) symmetry is broken, and a high-temperature paramagnetic phase. A key feature of the system is the separation of energy scales for charge and spin excitations, which is reflected in the temperature dependence of thermodynamic quantities and the disparity between spin and charge gaps extracted from their respective susceptibilities. At the critical point, both spin and charge susceptibilities exhibit singularities, suggesting that charge excitations are not fully decoupled from their spin counterparts. Additionally, the double occupancy number exhibits a nonmonotonic temperature dependence, indicative of an entropy-driven Pomeranchuk effect. These results demonstrate that the loopless Bethe lattice effectively captures the essential physics of the Hubbard model while providing a computationally efficient framework for studying strongly correlated electronic systems.

The electronic structure of the lightly hole-doped triangular-lattice moiré Hubbard model is studied within cluster perturbation theory (CPT) using 13-site clusters for a fixed doping concentration $p=1/13$ varying the Coulomb parameter $U$ and the hopping phase parameter $\varphi$ related to the spin-orbital interaction. We have also developed a rather simple generalized mean-field approximation (GMFA) containing the amplitude of the spin correlations as a free parameter to fit the CPT data. The evolution of the Fermi surface and the pseudogap with the parameters $\varphi$ and $U$ is explained from the viewpoint of the short-range magnetic order. The geometric frustration and the additional model parameter related to the spin-orbital interaction result in a more rich physics of the pseudogap state compared to the case of a more conventional square lattice.

Half-Heusler compounds are a class of materials with great potential for the study of distinct electronic states. In this work, we investigate, from first-principles, the possibility of hinge modes in closely related topological phases that are tunable by moderate uniaxial strain. We consider two compounds: LiSbZn and LiBiZn. While LiSbZn has a topologically trivial band structure, the larger spin-orbit coupling of Bi causes a band inversion in LiBiZn. We predict the existence of topologically trivial hinge states in both cases. The hinge modes are affected by both the crystal termination and the bulk topological phase transitions, albeit indirectly: when present, topological surface modes hybridize with the hinge states and obscure their visibility. Thus, we find that the most visible hinge modes occur when no band inversions are present in the material. Our work highlights the interplay and competition between surface and hinge modes in half Heuslers, and may help guide the experimental search for robust boundary signatures in these materials.

The accurate determination of non-Hermitian (NH) topological invariants plays a central role in the study of NH topological phases. In this work, we propose a general framework for directly measuring NH topological invariants in even-dimensional systems with real line gaps through quench dynamics. Our approach hinges on constructing an auxiliary Hermitian matrix topologically equivalent to the original NH Hamiltonian, enabling topological characterization via reduced-dimensional momentum subspaces called band-inversion surfaces (BISs). A key insight lies in the emergence of chiral symmetry in the NH Hamiltonian specifically on BISs—a critical property that allows extension of the dynamical characterization scheme previously developed for odd-dimensional NH systems with chiral or sublattice symmetry [Lin et al., Phys. Rev. Res. 7, L012060 (2025)]. We show that NH topological invariants can be extracted from the winding patterns of a dynamical field constructed from post-quench spin textures on BISs. We demonstrate our approach through a detailed analysis of NH Chern insulators and then extend the framework to higher even-dimensional systems by introducing second-order BISs for characterization. The framework is also generalized to imaginary line-gapped topological phases. This work establishes an experimentally accessible protocol for detecting NH topological invariants in quantum platforms.

We theoretically investigate three-dimensional singular flat band systems, focusing on their quantum geometric properties and response to external magnetic fields. As a representative example, we study the pyrochlore lattice, which hosts a pair of degenerate flat bands touching a dispersive band. We derive a three-orbital effective continuum model that captures the essential features near the band-touching point. Within this framework, we identify the point-like topological singularity on a planar manifold defined by the degenerate flat band eigenvectors. This singularity strongly influences the quantum geometry and results in a characteristic Landau level structure, where the levels spread over a finite energy range. We show that this structure reflects the underlying band reconstruction due to the orbital Zeeman effect, which lifts the flat band degeneracy and induces the Weyl-semimetal-like dispersion near the singularity. Our analysis reveals that the range of Landau level spreading is proportional to the quantum metric of each Zeeman-split band. We further demonstrate that adding a small dispersion via longer-range hopping induces unconventional Shubnikov-de Haas oscillations with a slowly drifting period. Finally, we show that our approach extends naturally to systems with higher orbital angular momentum, indicating the robustness of these features in a broad class of three-dimensional flat band models.

We consider thermo-optic bistability in the resonant excitation of high-quality modes in two-dimensional dielectric resonators. We develop a coupled-mode theory approach which account for the frequency shift due to a temperature-dependent dielectric permittivity. The model is applied to rectangular and hexagonal resonators supporting an isolated high-quality resonant mode. The results are verified in comparison with straightforward finite-element simulations. It is shown that the model accurately describes the effect of bistability which occurs under variation of the angle of incidence or the intensity of the incident wave. In particular, it is demonstrated that variation of the incident angle can optimize the coupling between the resonator and the incident waves leading to bistability with low-intensity incident waves, $W_0=0.35{\mu \mathrm{W}/\mu \mathrm{m}}^2$. The bistability threshold is shown to be extremely sensitive to the imaginary part of the dielectric permittivity ${\epsilon }^{″}$.

Phthalocyanine (${\mathrm{H}}_2\mathrm{Pc}$) based molecules are widely used as model systems in scanning tunneling microscopy (STM) based surface characterizations. In the present work, we carried out theoretical simulations on the STM images of ${\mathrm{H}}_2\mathrm{Pc}$ and deprotonated phthalocyanine (${\mathrm{HPc}}^{-}$) molecules by combining density functional theory calculations with Bardeen's approximation. The obtained STM images for the frontier molecular orbitals of the molecular systems resemble nicely the previously reported experimental features. It was found that the deprotonation process can lead to more profound effects for the lowest unoccupied molecular orbital (LUMO). Particularly, the ringlike feature in the central cavity of ${\mathrm{H}}_2\mathrm{Pc}$ as found in the LUMO was reduced to a half ring that is most bright in the position of the removed proton in ${\mathrm{HPc}}^{-}$, which corrects the intuitive assignment in the previous studies. The position and shape of the half ring feature in the central cavity coincide with the spatial distribution of the high negative values in the electrostatic potential of the molecule. Detailed analysis suggests that such a feature should be attributed to the asymmetric distribution of the wave function of the LUMO in the cavity of the deprotonated ${\mathrm{HPc}}^{-}$. Raman images for vibrational modes associated with the central H atoms of the two molecular systems were also simulated based on an effective field Hamiltonian. The good correspondence between the Raman images and the molecular vibrations suggests it could be applied to decisively identify the position of the remaining H atom in the ${\mathrm{HPc}}^{-}$.

The kagome lattice is renowned for its exotic electronic properties, such as flat bands, Dirac points, and Van Hove singularities. These features have provided a fertile ground for exploring exotic quantum phenomena. Here, we discover that a breathing kagome lattice with long-range hoppings can host multiple zero-energy corner states, which emerge as topologically protected bound states in the continuum (BICs). This result demonstrates that additional hopping control can induce further nontrivial physics of the kagome lattice. Since the zero-energy corner states in the continuum are intertwined with a substantial number of zero-energy bulk states, we also develop a momentum-space topological characterization theory to precisely quantify the number of corner states, revealing a general bulk-corner correspondence. Furthermore, we uncover three distinct types of topological phase transitions (TPTs) for the BICs driven by shifts in the spatial localization of zero-energy bulk and/or edge states. These TPTs are exactly captured by our characterization theory. This Letter provides deep insights into the topological physics of the kagome lattice and broadens the understanding of its electronic properties.

Charge density waves (CDWs)—collective quantum states arising from coupled electron-lattice interactions—serve as critical probes of competing orders in quantum materials, including superconductivity and magnetism. Monolayer $1T\text{−}\mathrm{VS}{\mathrm{e}}_2$ presents a unique platform where CDWs display substrate-sensitive configurations distinct from bulk systems, challenging conventional formation paradigms. Through scanning tunneling microscopy, we reveal how uniaxial strain controls CDW dimensionality and periodicity in monolayer $1T\text{−}\mathrm{VS}{\mathrm{e}}_2$, generating two strain-direction-dependent stripelike phases: an incommensurate one-dimensional (1D) CDW ($|Q_1|=1/\sqrt{7}\left|a^{*}\right|$) at 30 ° strain orientation and a commensurate 1D CDW $\left(Q_2=0.25a^{*}\right)$ aligned with lattice vectors. These directional modulations stem from strain-enhanced momentum-selective electron-phonon coupling, which overrides traditional Fermi surface nesting mechanisms. Furthermore, we reveal that coexisting complex CDW features, previously observed, are fundamentally emergent moiré patterns resulting from the superposition of engineered 1D CDWs and the underlying atomic lattice. Our work resolves longstanding controversies in monolayer $1T\text{−}\mathrm{VS}{\mathrm{e}}_2$ and provides a universal framework for manipulating correlated phases in van der Waals materials through anisotropic lattice engineering.

The control over quantum entanglement is fundamental to the advancement of large-scale quantum technologies. Here, we propose a chiral Majorana interferometer to govern the entanglement in a hybrid device consisting of a magnetic topological insulator and chiral topological superconductor. We show that quasiparticles outgoing from the domain wall of a chiral topological superconductor possess Nambu spinor entanglement because of the interference of chiral Majorana modes. It is found that the outgoing state can be manipulated continuously from the maximally entangled Bell state to the separable state by tailoring the type, thickness, and length of the domain wall. Based on the Clauser-Horne-Shimony-Holt inequality, it is shown that the concurrence quantifying the entanglement is directly given by the maximal Bell parameter measured from the current-current correlators.

Effective light cones, characterized by Lieb-Robinson bounds, emerge in nonrelativistic local quantum systems. Here, we present several analytical results derived from logarithmic light cones (LLCs). Possible origins of LLCs include the one-dimensional (1D) disordered XXZ model and a phenomenological model of many-body localization (MBL). In the LLC regime, we prove that, for arbitrary spatial dimensions and any initial pure state, entanglement growth is upper bounded by logarithmic time with an additional subleading double-logarithmic correction—arising from a real asymptotic solution of the Lambert W function—valid up to the asymptotic time limit. In the context of the 1D disordered XXZ model, this result resolves the ambiguity in distinguishing between logarithmic and power-law fits of entanglement growth in numerical studies; we also propose a falsifiable phenomenological functional form for the entanglement growth that agrees with existing numerical results. We show that information scrambling is logarithmically slow in the LLC regime. Furthermore, we demonstrate that the LLC supports long-lived quantum memories—quantum codes with macroscopic code distance and lifetimes that scale exponentially with system size—under unitary time evolution. Our analytical results provide benchmarks for future numerical studies of the MBL regime at large timescales.

It is a central problem in various fields of physics to elucidate the behavior of quantum many-body systems subjected to bulk dissipation. In this context, several microscopic derivations of the Lindblad quantum master equation for many-body systems have been proposed so far. Among them, the universal Lindblad equation derived by Nathan and Rudner is fascinating because it has the desired locality and its derivation seems to rely solely on the assumption that the bath correlation time is much shorter than the dissipation time, which is the case in the weak-coupling limit or the singular-coupling limit. However, it remains elusive whether errors from several approximations in deriving the universal Lindblad equation remain small during the time evolution in the thermodynamic limit. Here, rigorous error bounds on the time evolution of a local quantity are given, and it is shown that, under the assumption of accelerated dissipation in bulk-dissipated systems, those errors vanish in the weak-coupling limit or the singular-coupling limit after taking the thermodynamic limit.

We investigated the spin-$\frac{1}{2}$ Heisenberg model with competing ferromagnetic and antiferromagnetic interactions on diamond-decorated lattices. Tuning the exchange interactions to the boundary of the ferromagnetic phase, we analyze the models with two types of diamond units: distorted and ideal diamonds. In the distorted diamond model, flat bands in the magnon spectra indicate the localized states confined to small regions (trapping cells) of the lattice. Remarkably, these trapping cells can host up to five and seven localized states for square and cubic lattices, respectively, leading to macroscopic ground state degeneracy and high values of residual entropy. The problem of calculating ground state degeneracy reduces to that of noninteracting spins, whose spin value is equal to half the number of localized magnons in the trapping cell. In contrast, ideal diamond models feature ground states composed of randomly distributed isolated diamond diagonal singlets immersed in a ferromagnetic background. Counting the ground state degeneracies here maps onto the percolation problem in two- and three-dimensional lattices. Our analysis shows that ideal diamond models possess even greater ground state degeneracy than their distorted counterparts. These findings suggest that the synthesizing of diamond-decorated type compounds holds great promise for low-temperature cooling applications.

Employing a combination of first-principles calculations and an ab initio derived model Hamiltonian study, we investigate the electronic and magnetic properties of the rare-earth antimonides ${\mathrm{LaCrSb}}_3, {\mathrm{CeCrSb}}_3$, and ${\mathrm{NdCrSb}}_3$. Our findings indicate that the long-range ferromagnetic order in these metallic compounds originates from a kinetic energy-driven double exchange mechanism, first proposed in the context of double perovskite compound ${\mathrm{Sr}}_2{\mathrm{FeMoO}}_6$. The calculated magnetic transition temperatures are in reasonable agreement with the measured values. The spin-orbit coupled band structure of the studied compounds reveals nontrivial topology, hosting multiple Weyl point crossings. The number of these crossings increases in moving from ${\mathrm{LaCrSb}}_3$ to ${\mathrm{CeCrSb}}_3$ to ${\mathrm{NdCrSb}}_3$, assisted by the lowering of the $5d$ states in nonzero $f$ rare-earth compounds. The calculated anomalous Hall conductivity captures experimentally observed large anomalous Hall conductivity in these compounds, and the trend between ${\mathrm{LaCrSb}}_3, {\mathrm{CeCrSb}}_3$, and ${\mathrm{NdCrSb}}_3$. Our study provides a microscopic understanding of the trend.

Superfluid density in quasi-one-dimensional boson systems with two different transverse density profiles is calculated: In one case, bosons fill a tube almost uniformly, and in the other case, bosons are restricted on the internal surface of a tube and form a film. In both cases, the superfluid density approaches the prediction by the Tomonaga-Luttinger liquid theory as the system length becomes long, and no evidence for the scaling behavior characteristic to the Berezinskii-Kosterlitz-Thouless transition is found in the case of a film. A dimensionless quantity characterizing the one-dimensionality is introduced in each case (a filled tube and a film).

We investigate the localization and topological properties of the nonequilibrium steady state (NESS) in a one-dimensional homogeneous system. Our results demonstrate that, despite the absence of disorder in the initial system, the NESS can exhibit localization under bond dissipation. These dissipation-driven localization and delocalization phenomena are clearly distinguished using Wigner distributions. Furthermore, we find that the initial localization characteristics of the system significantly influence the localization properties of the NESS. Drawing upon the concept of Bose-Einstein condensate broadening in cold-atom experiments, along with experimental data, we systematically characterize the impact of bond dissipation and disorder on the localization and topological properties of the NESS. The phase diagram reveals that the NESS can be topologically nontrivial even when the initial system is topologically trivial, and that the topological triviality of the initial system strengthens the topological nontriviality of the NESS. This work provides insights into the localization and topological phase transitions in homogeneous systems induced by bond dissipation and disorder.

In $3d$-electron magnetic systems, the magnetic structures that transform each other by spin rotation have very close degenerate energies due to small spin-orbit coupling and can be easily controlled by chemical substitution and external magnetic fields. We investigate anisotropic piezomagnetic effects, exhibiting the different magnetic responses depending on the type of strain and the magnetic structures, for noncollinear magnetic states in ${\mathrm{Mn}}_{3}A\mathrm{N}$ ($A=$ Ni, Cu, Zn, Ga) and ${\mathrm{Mn}}_{3}X$ ($X$= Sn and Ge) based on detailed symmetry analysis using spin group and magnetic group and first-principles calculations of piezomagnetic responses. In ${\mathrm{Mn}}_{3}A\mathrm{N}$, magnetization develops along two distinct directions under the same applied stress, corresponding to two AFM states connected by spin rotation. Analysis of the piezomagnetic tensor based on magnetic and spin point groups for the states with and without spin-orbit coupling, respectively, shows that the difference in the magnitude of magnetization along different directions is attributed to the spin-orbit coupling. ${\mathrm{Mn}}_{3}X$ are known to stabilize different AFM structures in the directions of the applied in-plane magnetic fields. Under uniaxial stress along the orthorhombic $x$- and $y$-axes, magnetization is induced without breaking the magnetic symmetry, but it develops in the opposite direction due to exchange interaction. Our study demonstrates that the direction and sign of strain-induced magnetization in ${\mathrm{Mn}}_{3}A\mathrm{N}$ and ${\mathrm{Mn}}_{3}X$ can be effectively controlled by strain in combination with magnetic fields. These findings highlight the potential for strain-tunable magnetic devices in noncollinear AFMs.