We develop a QR-based corner transfer matrix renormalization group (CTMRG) framework for contracting infinite projected entangled-pair states on honeycomb lattices. Our method explicitly uses the lattice's native ${\mathrm{C}}_{3v}$ symmetry at each site, generalizing QR-based acceleration (previously limited to square lattices) to enable efficient and stable contractions. This approach achieves order-of-magnitude speedups over conventional singular value decomposition-based CTMRG while maintaining high numerical precision. Comprehensive benchmark calculations for the spin-1/2 Heisenberg and Kitaev models demonstrate higher computational efficiency without sacrificing accuracy. We further employ our method to study the Kitaev-Heisenberg model, where we provide numerical evidence for the universal $1/r^4$ decay of the dimer-dimer correlation function within the quantum spin liquid phase. Our work establishes a framework for extending QR-based CTMRG to other lattice geometries, opening alternative avenues for studying exotic quantum phases with tensor networks.

Coupled layer constructions are a valuable tool for capturing the universal properties of certain interacting quantum phases of matter in terms of the simpler data that characterizes the underlying layers. In the study of fracton phases, the X-cube model in $3+1\mathrm{D}$ can be realized via such a construction by starting with a stack of $2+1\mathrm{D}$ toric codes and turning on a coupling that condenses a composite “particle-string” object. In a recent work [Phys. Rev. B 112, 125124 (2025)], we have demonstrated that in fact, the particle string can be viewed as a symmetry defect of a topological 1-form symmetry. In this paper, we study the result of gauging this symmetry in depth. We unveil a rich gauging web relating the X-cube model to symmetry-protected topological (SPT) phases protected by a mix of subsystem and higher-form symmetries, subsystem symmetry fractionalization in the $3+1\mathrm{D}$ toric code, and nontrivial extensions of topological symmetries by subsystem symmetries. Our work emphasizes the importance of topological symmetries in nontopological, geometric phases of matter.

A theory of dynamic polarization of the nuclear spin system via optically oriented charge carriers in lead halide perovskites is developed and compared with the experiments performed on a ${\mathrm{FA}}_{0.9}{\mathrm{Cs}}_{0.1}{\mathrm{PbI}}_{2.8}{\mathrm{Br}}_{0.2}$ crystal. The spin Hamiltonians of the electron and hole hyperfine interaction with the nuclear spins of lead and halogen are derived. The hyperfine interaction of the halogen spins with charge carriers is shown to be anisotropic and depending on the position of the halogen nucleus in the cubic elementary cell. The quadrupole splitting is absent for the lead spins, but plays an important role for the halogen spins and affects their dynamic polarization by charge carriers. The Overhauser fields of the dynamically polarized nuclei are calculated as functions of the tilting angle of an external magnetic field and compared with the experimentally measured angular dependence of the Hanle effect. The comparison of the theoretical model with the experimental data reveals an enhanced spin polarization of the lead nuclei, whose mean spin exceeds several times the mean spins of localized electrons and holes. This unexpectedly strong spin polarization is explained by the interaction of the lead nuclei with excitons having a high degree of spin orientation because of their short lifetime after excitation by circularly polarized light. The dynamic polarization of the quadrupole-split halogen spins manifests itself via the magnetic field they produce at the lead nuclei. This field maintains the magnetization of the lead nuclei at zero external magnetic field. The dynamics of the nuclear spin polarization is measured under optical pumping and in the dark, yielding a nuclear spin-lattice relaxation time on the order of 10 seconds.

We investigate the topological electronic properties of the $K_4$ crystal by constructing a tight-binding model. The bulk band structure hosts Weyl nodes with higher and conventional chiralities ($\chi =\pm 2$ and $\chi =\pm 1$) located at high-symmetry points in the Brillouin zone. Through analytical evaluation of the Berry curvature, we identify the positions and chiralities of these Weyl nodes. Furthermore, slab calculations for the (001) surface reveal Fermi arcs that connect Weyl nodes of opposite chirality, including those linking $\chi =\pm 2$ nodes with pairs of $\chi =\mp 1$ nodes. These results demonstrate that the $K_4$ crystal is a spinless Weyl semimetal featuring topologically protected surface states originating from multiple types of Weyl nodes.

This work focuses on the nondissipative, parity-odd spin transport of $(2+1)$-dimensional relativistic electrons, generated by torsion, and the torsional Hall viscosity ${\zeta }_{\mathrm{H}}$. We first determine ${\zeta }_{\mathrm{H}}$ for massive Dirac fermions in the presence of a constant electromagnetic field. We predict that the magnetic field induces a contribution to ${\zeta }_{\mathrm{H}}$ competing with the one originating from the Dirac mass. Moreover, we quantify the impact on ${\zeta }_{\mathrm{H}}$ originating from the band structure deformation quadratic in momentum terms that was proposed by Bernevig-Hughes-Zhang (BHZ). We find that the BHZ deformation substantially enhances ${\zeta }_{\mathrm{H}}$ in magnitude as measured in a domain wall configuration, when compared to the free Dirac fermion result. Nevertheless, the torsional Hall viscosity still discriminates between topologically trivial and nontrivial regimes. Our results, hence, pave the way for a deeper understanding of hydrodynamic spin transport and its possible verification in experiments.

Altermagnets host unconventional spin-polarized bands despite zero net magnetization, but controlling their spin structure remains challenging. We theoretically propose a multifield approach to engineer spin polarization in $d$-wave altermagnets using gating, optical driving, and in-plane electric fields, which enable tunable and switchable polarizations along multiple directions. Optical driving induces out-of-plane ($z$) polarization, while gating and in-plane fields generate $x$ and $y$ polarizations via the Edelstein effect, all of which are experimentally detectable. We further find that spin- and band-selective doping induces chiral optical activity, a feature unique to altermagnets. Our approach offers a versatile means to control the direction of spin polarization in altermagnets.

Cadmium sulfide (CdS), which exhibits a wurzite (WZ) to rocksalt (RS) phase transformation at elevated stresses, is an ideal system to address the role of deformation on phase transformation mechanisms and kinetics. CdS has been shown to have very different elastic-inelastic behavior for shock propagation along the WZ $c$- and $a$-axes, and also exhibits significant differences in the time scale for the phase transformation when shocked along these different axes. As an important first step in examining the role of deformation in shock-induced phase transformations, here we present in situ, time-resolved x-ray diffraction (XRD) measurements in single-event, shock wave experiments on CdS single crystals shocked along the WZ $c$-axis to elastic impact stresses near or above $\sim 5\mathrm{GPa}$, where a marked increase in the kinetics of this transformation has been reported. The XRD measurements are compared with forward diffraction simulations to evaluate different proposed phase transformation mechanisms and are shown to be consistent with a shearing mechanism that results in the RS [001] direction being aligned with the original WZ $c$-axis and the RS [110] direction being aligned with the original WZ $a$-axis. In order to reproduce all observed RS diffraction spots the forward diffraction simulations required three different RS crystalline domains, each with a [110] direction aligned with one of the three original WZ $a$-axes, and a significant mosaicity, particularly about the RS [001] direction (the direction of shock propagation). This large mosaicity is likely due to variations in the possible shearing mechanisms that connect the WZ and RS structures, which can create crystallites with up to $\sim \pm {10}^{\circ }$ of relative rotations about the RS [001] direction, as well as further rotation of these crystallites as they grow, merge, and coalesce.

The hydrogen diffusion in NiO is closely relevant to various applications of Ni-based metals, which are inevitably passivated by native oxides. The precise description of hydrogen diffusion in NiO is always complicated by the coexistence of many influential electronic-structure and lattice-dynamics mechanisms, which are unraveled by the combinatorial first-principles calculations based on density-functional theory (DFT) here. Firstly, based on two widely recognized semilocal density functionals (i.e., PBE and PBEsol), the electronic correlation potential for the $\mathrm{Ni}\text{−}3d$ orbital is efficiently described by the $\mathrm{DFT}+U$ model, with the Hubbard-$U$ value determined by using the linear-response theory. The benchmark calculations of crystal structure, bulk modulus, electronic-structure properties, vibrational spectra, and thermal expansion of NiO comprehensively confirm the high systematic accuracy of $\mathrm{PBEsol}+U$ model. Then, it is used to calculate the diffusion paths, kinetic energies, and diffusion rates of H in NiO, where the synergistic effects of multiple factors (e.g., electronic correlation, interatomic bonding, magnetic superexchange interaction, local lattice distortion, atomic vibrations, and thermal expansion) are quantitatively portrayed. The high directional anisotropy is found in the hydrogen diffusion paths and is attributed to the magnetic anisotropy in NiO, allowing the kinetic tunability by thermal and magnetic-field manipulations. A kinetic Monte Carlo method is designed to simulate the multiscale diffusion behaviors of H in NiO, and to yield the diffusion coefficients. A spatial-dimensionality transition is discovered in the simulated diffusion trajectories of H upon heating. Finally, the isotope effects on hydrogen-diffusion rates are also predicted, and will be important for many radioactive situations.

Periodic drive is an intriguing way of creating topological phases in a nontopological setup. However, most systems are often studied as a closed system, despite being always in contact with the environment, which induces dissipation. Here, we investigate a periodically driven Rashba nanowire in proximity to an $s$-wave superconductor in a dissipative background. The system's dynamics is governed by a periodic Liouvillian operator, from which we construct the Liouvillian time-evolution operator and use the third-quantization method to obtain the ‘‘Floquet damping matrix’’, which captures the spectral and topological properties of the system. We show that the system exhibits edge-localized topological Majorana 0-modes (MZMs) and $\pi$-modes (MPMs). Additionally, the system also supports a trivial 0-modes (TZMs) and $\pi$-modes (TPMs), which are also localized at the edges of the system. The MZMs and the MPMs are connected to the bulk topology and carry a bulk topological invariant, while the emergence of TZMs and TPMs is primarily tied to exceptional points and is topologically trivial. We show that both the topological (MZMs and MPMs) and trivial (TZMs and TPMs) edge modes are robust against onsite disorder. We study the topological phase diagrams in terms of the topological invariants and show that the dissipation can modify the topological phase diagram substantially and even induce topological phases in the system. Our work extends the understanding of a driven-dissipative topological superconductor.

Neutron diffraction experiments of ${\mathrm{TmFeO}}_3$ single crystals were performed in the external magnetic fields. The field along the $c$ axis increases temperature of spin-reorientation transition $T_{\text{SR}}$ from phase $\mathrm{\Gamma }4$ to $\mathrm{\Gamma }2$. Application of the field along $b$ axis led to the decrease of $T_{\text{SR}}$ and to the formation of new phases. Based on the temperature and field dependence of the Bragg reflection intensity, the configuration of magnetically induced phases was proposed.

The vast majority of symmetry-protected topological (SPT) states are difficult to detect, which often leads to their misidentification as ordinary or topologically trivial phases. In this work, we propose a general framework for detecting these hidden topological states. We distinguish the ordinary matter state from the topological phase by exploiting the boundary effects in space (via surface behaviors on engineered edge) and time (via strange correlators) according to the principle of bulk-edge correspondence. As a concrete example, we study the dimerized spin-1/2 Heisenberg model on a square lattice using quantum Monte Carlo simulations, focusing on its paramagnetic dimer phase and edge states. The dimer phase has been widely regarded as topologically trivial due to its gapped edge state on conventional edges. However, the model can also be viewed as two-dimensional antiferromagnetically coupled typical ladders, which suggests an SPT state adiabatically connected to the one-dimensional Haldane phase. We resolve this puzzle and demonstrate that the dimer phase is indeed a quasi-one-dimensional SPT state by measuring generalized strange correlators introduced in this work and by showing that the nontrivial gapless edge state on a zigzag edge is ferromagnetically ordered, resulting from effective ferromagnetic interactions between degenerate spinons liberated on each side of the cut. Furthermore, we show that the ordered edge state gives rise to an extraordinary surface critical behavior at the ($2+1$)-dimensional O(3) bulk critical points of the model, which contradicts theoretical predictions based on classical-quantum mapping. Overall, we establish a standard detection method for uncovering topological phases that masquerade as ordinary states of matter.

Higher-order Van Hove singularities in strongly correlated electron systems provide a fertile ground for emergent electronic orders and superconductivity. This study investigates the interplay between magnetic fluctuations and superconducting pairing near higher-order Van Hove singularities on the honeycomb lattice, a paradigmatic platform relevant to graphene. By incorporating third-nearest-neighbor hopping $t^{\prime \prime }$, we uncover a universal crossover: ferromagnetic fluctuations dominate below the higher-order Van Hove filling, while antiferromagnetic fluctuations take over toward half filling. A key finding is that the already dominant $f_n$-wave pairing is enhanced in the critical region of this magnetic crossover by the higher-order Van Hove. This enhancement is driven by the synergistic effect of the higher-order Van Hove singularities-induced divergent density of states and the competing magnetic fluctuations. Although increased hopping parameters generally suppress superconducting correlation, we identify a critical $t^{\prime \prime }$ that anomalously enhances pairing via the higher-order Van Hove renormalization. Furthermore, the nearest-neighbor Coulomb interaction suppresses the pairing correlation function in a sign-independent manner. Our results clarify the competitive mechanisms between magnetic fluctuations and unconventional superconductivity in higher-order Van Hove singularities systems, offering a theoretical basis for tailoring quantum phases in graphene-based materials via band engineering.

Single-crystal x-ray diffraction (XRD) measurements were conducted on quasi-two-dimensional organic salt ${\alpha }^{\prime }\text{−}{\left(\mathrm{ET}\right)}_2{\mathrm{IBr}}_2$ to investigate the charge ordering (CO) pattern, which remained unresolved by local probes, and the anomalous absence of second-harmonic generation (SHG) signal at intermediate temperature ($160\text{K}<T<200\text{K}$). Our structural analysis at 110 K reveals a noncentrosymmetric horizontal stripe type CO pattern with a charge separation ($\mathrm{\Delta }\rho =|{\rho }_{\text{rich}}-{\rho }_{\text{poor}}|$) of $\mathrm{\Delta }\rho \approx 0.8e$. These findings are consistent with results from ${}^{13}\mathrm{C}\text{−}\mathrm{NMR}$, vibrational spectroscopy, and the observation of finite SHG signal. At intermediate temperature, SHG signal was absent despite the presence of CO, indicating a superstructure with antiparallel polarization. However, there was no direct structural evidence, including phase transition and CO pattern at 200 K. A superlattice structure with lattice doubling along the $c$ axis was identified in the intermediate temperature range ($160\text{K}<T<200\text{K}$). The structural analysis at 180 K confirms that the charge ordered layers are related by an inversion center and exhibit a horizontal stripe type CO pattern, explaining the absence of SHG signal in this phase. Those findings establish three distinct structural and electronic phases in ${\alpha }^{\prime }\text{−}{\left(\mathrm{ET}\right)}_2{\mathrm{IBr}}_2$. Furthermore, the suppression of dynamic ethylene group disorder below 200 K was observed, suggesting a possible contribution to the previously reported Raman spectral broadening of the anion. This offers an alternative explanation to the previous model based on dynamic charge fluctuations.

The recent realization that the rare-earth melilites ${\mathrm{RE}}_2{\mathrm{Be}}_2{\mathrm{GeO}}_7$ host the Shastry-Sutherland lattice within planes of ${\mathrm{RE}}^{3+}$ ions has sparked a number of studies. This family of materials lacks appreciable site mixing and conductivity, making them promising candidates for the Shastry-Sutherland model. Herein, we present the magnetic ground states of two of these rare-earth melilites: RE = Gd and Dy. We find, through measurements of magnetic susceptibility, magnetization, and specific heat capacity (RE = Dy only), that these two melilites are antiferromagnets ($T_N \approx 1$ K). ${\mathrm{Gd}}_2{\mathrm{Be}}_2{\mathrm{GeO}}_7$, in accordance with its electronic configuration, has isotropic single-ion anisotropy but shows a quadratic contribution to its magnetization. ${\mathrm{Dy}}_2{\mathrm{Be}}_2{\mathrm{GeO}}_7$ has Ising-like single-ion anisotropy and is likely an effective spin-$1/2$ system. Both materials exhibit metamagnetic transitions. We identify this transition in ${\mathrm{Dy}}_2{\mathrm{Be}}_2{\mathrm{GeO}}_7$, occurring at 86(1) mT for $T=500$ mK, to likely be a spin-flip transition.

We develop a theoretical and numerical framework for three-dimensional bulk chiral magnets that includes the full magnetostatic dipole-dipole interaction and its back-reaction on the magnetization. Assuming translational invariance along one spatial direction, we analyze the effect of dipolar interactions on three Dzyaloshinskii-Moriya interaction (DMI) terms—Dresselhaus, Rashba, and Heusler—corresponding to Bloch, Néel, and antiskyrmion textures. In the absence of the dipolar interaction, these three DMI terms are gauge equivalent and yield degenerate skyrmion energies. Incorporating the nonlocal dipole-dipole interaction breaks this degeneracy: Bloch skyrmions remain unaffected, Néel skyrmions shrink slightly, and Heusler antiskyrmions lose axial symmetry and stabilize into square lattice crystals. The system is solved using a nonlocal numerical relaxation method that self-consistently computes the magnetostatic potential from Poisson's equation. Our results show that long-range dipolar interactions can stabilize bulk antiskyrmion crystals in translationally invariant three-dimensional chiral magnets.

Symmetry-resolved entanglement entropy provides a powerful framework for probing the internal structure of quantum many-body states by decomposing entanglement into contributions from distinct symmetry sectors. In this work, we apply matrix product state techniques to study the bosonic, non-Abelian Moore-Read quantum Hall state, enabling precise numerical evaluation of both the full counting statistics and symmetry-resolved entanglement entropies. Our results reveal an approximate equipartition of entanglement among symmetry sectors, consistent with theoretical expectations and subject to finite-size corrections. The results also show that these expectations for symmetry-resolved entanglement entropy remain valid in the case of a non-Abelian state where the topological sectors cannot be distinguished by the Abelian $\mathrm{U}\left(1\right)$ symmetry alone, and where neutral and charged modes possess distinct velocities. We additionally perform a detailed comparison of the entanglement spectrum with predictions from the Li-Haldane conjecture, finding remarkable agreement, and enabling a more precise understanding of the effects of the distinct neutral and charged velocities. This not only provides a stringent test of the conjecture but also highlights its explanatory power in understanding the origin and structure of finite-size effects across different symmetry sectors.

By utilizing the site-dependent spin quantization axis in semiconductor quantum dot (QD) arrays, shuttling-based spin qubit gates have become an appealing approach to realize scalable quantum computing due to the circumvention of using high-frequency driving fields. The emergence of a spin deviation from the local quantization axis of one residing QD is the prerequisite to implement the qubit gates. In this work, we study the nonadiabatic dynamics of a spin qubit shuttling between coupled QDs with inhomogeneous Landé $g$ tensors and a small magnetic field. The spin dynamics is analyzed through solving the time-dependent Schrödinger equation of the qubit under the effects of spin-orbit interaction and rapid ramping interdot detuning. The precondition, imposed on the ramping time and the tunnel-coupling strength, to ensure a high-fidelity interdot transfer is estimated. We then calculate the change in the spin orientation of a transferred qubit and study the dependencies of the spin deviation on the difference in the quantization axes of the two QDs, the tunnel-coupling strength, and the ramping time. We also demonstrate that the effect of multiple rounds of interdot bidirectional shuttling can be captured by an operator matrix, and evaluate the idling times required for realizing the single-qubit Pauli-$X$ and Pauli-$Y$ gates. Intriguingly, it is confirmed that a generalized Hadamard gate can be achieved through tuning the idling times.

In recent years, non-Hermitian systems and artificial gauge fields have made possible realization of continuous Landau modes (CLMs), which exhibit Gaussian spatial envelopes and continuous spectra in the complex plane. However, existing studies on CLMs have mostly focused on the analysis of band structures in two-dimensional (2D) systems; it is a challenge to achieve spatial energy localization, especially multipoint energy concentration in the form of a wave funnel effect. In this work, we propose and experimentally demonstrate a circuit-based design framework that successfully realizes CLMs in one-dimensional and 2D topolectrical circuits. By introducing a spatial gradient of resistors, we implement non-Hermiticity and pseudomagnetic field, thereby establishing the necessary conditions for CLMs. More importantly, through carefully engineered inductor-capacitor coupling, we observe a dual-frequency wave funnel phenomenon, where wave energy becomes strongly concentrated at two distinct locations along the boundary with the lowest loss. Our results reveal an extension of Landau physics in discrete artificial systems and offer an effective approach for achieving multipoint spatial energy localization in circuit platforms.

Polariton canalization exhibits highly collimated and diffraction-free propagation characteristics in natural hyperbolic materials, holding great promise for molding the energy flow at nanoscale. Previously, the majority of canalizations were realized in phonon polaritons. Herein, we theoretically explore hyperbolic magnetoexciton polaritons (HMEPs) in van der Waals crystals of ${\mathrm{WTe}}_2, {\mathrm{MoS}}_2$, and phosphorene. Based on the Shubnikov–de Haas effect, canalized HMEPs with ultralow group velocity ($\sim {10}^{-5}c$) and superlong lifetimes (hundreds of microseconds) are predicted at low temperatures. We also show that the inter-Landau-level transitions and nonlocal dielectric screening effect significantly modify the optical topologies of canalized HMEPs, manifested by various exotic isofrequency contours (IFCs) including hyperbolic, witch-of-Agnesi, one-sheet, two-fold, and twisted pincerlike IFCs. Our findings reveal the significant effects of magneto-optical transport on hyperbolic polaritons, which not only enrich the interplay mechanism between magnetics and polaritonics but also provide a promising playground for future developments in hyperbolic materials.

We study multiplicative Chern insulators (MCIs) as canonical examples of multiplicative topological phases of matter. Constructing the MCI Bloch Hamiltonian as a symmetry-protected tensor product of two topologically nontrivial parent Chern insulators (CIs), we study two-dimensional (2D) MCIs and introduce three-dimensional mixed MCIs, constructed by requiring the two 2D parent Hamiltonians share only one momentum component. We study the 2D MCI response to time-reversal symmetric flux insertion, observing a $4\pi$ Aharonov-Bohm effect, relating these topological states to fractional quantum Hall states via the microscopic field theories of the quantum skyrmion Hall effect. As part of this response, we observe evidence of quantization of a proposed topological invariant for compactified many-body states to a rational number, suggesting higher-dimensional topology may also be relevant. Finally, we study effects of bulk perturbations breaking the symmetry-protected tensor-product structure of the child Hamiltonian, finding the MCI evolves adiabatically into a topological skyrmion phase.