The traditional systems researched in condensed matter physics always have spatial translation symmetry. However for space-time crystal systems, the spatial translation symmetry is no longer preserved and the lattice potential has space-time translation symmetry instead. We show that a rational space-time crystal system is equal to a traditional Floquet system. Then, we find a way to solve the Floquet equation analytically and construct an effective Hamiltonian of the rational space-time crystal system. By this effective Hamiltonian, we obtain the topological classification of gapped and gap-preserving rational space-time crystal systems. Our work reveals the correlation between space-time crystal systems and Floquet systems and gives a systematic method to explore the properties of rational space-time crystal systems.

The $S=1$ bilinear-biquadratic Heisenberg exchange model on the triangular lattice with a single-ion anisotropy has previously been shown to host a number of exotic magnetic and nematic orders [Moreno-Cardoner et al., Phys. Rev. B 90, 144409 (2014)], including an extensive region of “supersolid” order. In this work, we amend the model by an $XXZ$ anisotropy in the exchange interactions. Tuning to the limit of an exactly solvable $S=1$ generalized Ising-/Blume-Capel-type model provides a controlled limit to access phases at finite transverse exchange. Notably, we find an additional macroscopically degenerate region in the phase diagram and study its fate under perturbation theory. We further map out phase diagrams as a function of the $XXZ$ anisotropy parameter, the ratio of bilinear and biquadratic interactions, and single-ion anisotropy, and we compute corrections to the total ordered moment in various phases using systematically constructed linear flavor-wave theory. We also present linear flavor-wave spectra of various states, finding that the lowest-energy band in three-sublattice generalized (i.e., with $S^z=\pm 1,0)$ Ising/Blume-Capel states, stabilized by strong exchange anisotropies, is remarkably flat, opening up the way to flat-band engineering of magnetic excitation via stabilizing nontrivial Ising-ordered ground states.

The strong correlation between the nontrivial band topology and the magnetic texture makes magnetic Weyl semimetals excellent candidates for the manipulation and detection of magnetization dynamics. The parity violation together with the Pauli blocking cause only one Weyl node to contribute to the photocurrent response, which in turn affects the magnetic texture due to the spin-transfer torque. Utilizing the Landau-Lifshitz-Gilbert equation and the spin-transfer torque in noncentrosymmetric Weyl magnets, we show that the chiral photocurrent rotates the magnetization from the easy $c$ axis to the $a$ or $b$ axis, which leads to an exotic current next to the photocurrent response. The chiral photocurrent is calculated in the context of quantum kinetic theory, and it has a strong resonance on the order of mA/W near the Weyl nodes, the magnitude of which is controlled by the momentum relaxation time. Remarkably, we study the influence of magnetic texture dynamics on the topological nonlinear photocurrent response, including shift and injection currents along with the new chiral photocurrent, and we show that both the magnitude and the in-plane orientation of the chiral photocurrent are strongly correlated with the direction of the magnetic moments.

We theoretically study the anomalous Hall effect (AHE) in perovskites with antiferromagnetic (AFM) orderings. By studying the multiorbital Hubbard model for $d$ electrons in perovskite transition metal oxides under the ${\mathrm{GdFeO}}_3$-type distortion within the Hartree-Fock approximation, we investigate the behavior of intrinsic AHE owing to the atomic spin-orbit coupling via the linear response theory. We consider the cases where there exist two ($d^2$) and three ($d^3$) electrons in the $t_{2g}$ orbitals, and show that AFM ordered states can exhibit AHE. In the $d^2$ case, $C$-type AFM states give rise to dc AHE in metals and optical (finite-$\omega$) AHE in insulators accompanying orbital ordering, while in the $d^3$ case, a $G$-type AFM insulating state supports the optical AHE. By resolving the components in the spin patterns compatible with the space group symmetry, we specify the collinear AFM component to be responsible for the AHE, rather than the small ferromagnetic component. We discuss the microscopic origin of the AHE: the collinear AFM spin structure produces a nonzero Berry phase from the triangular units of the lattice, activated by the complex orbital mixing terms owing to the ${\mathrm{GdFeO}}_3$-type distortion, and results in the microscopic Lorentz force.

As a prototype system of the quantum spin Hall effect, the Kane-Mele model which was proposed initially in graphene promotes the search for two-dimensional topological materials of hexagonal lattices. Here we generalize the Kane-Mele model to exotic amorphous systems which possess a remarkable structural property called hyperuniformity. We show that, in general, the Quantum spin Hall state still survives in disordered hyperuniform lattices that are constructed by structural transformation involving Stone-Wales defects. However, compared to that in the honeycomb lattice, the gapped topological region in the phase diagram shrinks and the size of the corresponding topological gap decreases remarkably in disordered hyperuniform lattices. By introducing random vacancies in either perfectly ordered or disordered hyperuniform lattices, we further show that the degradation or destruction of hyperuniformity is detrimental to the existence of gapped topological states. We therefore propose that the hyperuniform metric of an amorphous lattice, which quantifies the extent of disordered hyperuniformity, reflects its ability to preserve topological states. Our finding not only establishes the possible underlying link between electronic topology and disordered hyperuniformity but also provides useful guidance for the seeking of topological materials in amorphous states of matter.

In this work, we focus on two questions. One, we complement the machinery to calculate geometric phases along adiabatic cycles as follows. The geometric phase is a line integral along an adiabatic cycle and if the cycle encircles a degeneracy point, the phase becomes nontrivial. If the cycle crosses the degeneracy point, the phase diverges. We construct quantities which are well defined when the path crosses the degeneracy point. We do this by constructing a generalized Bargmann invariant and noting that it can be interpreted as a cumulant generating function, with the geometric phase being the first cumulant. We show that particular ratios of cumulants remain finite for cycles crossing a set of isolated degeneracy points. The cumulant ratios take the form of the Binder cumulants known from the theory of finite size scaling in statistical mechanics (we name them geometric Binder cumulants). Two, we show that the developed machinery can be applied to perform finite size scaling in the context of the modern theory of polarization. The geometric Binder cumulants are size independent at gap-closure points or regions with closed gap (Luttinger liquid). We demonstrate this by model calculations for a one-dimensional topological model, several two-dimensional models, and a one-dimensional correlated model. In the case of two dimensions, we analyze to different situations, one in which the Fermi surface is one dimensional (a line) and two cases in which it is zero dimensional (Dirac points). For the geometric Binder cumulants, the gap-closure points can be found by one-dimensional scaling even in two dimensions. As a technical point, we stress that only certain finite difference approximations for the cumulants are applicable since not all approximation schemes are capable of extracting the size scaling information in the case of a closed-gap system.

A formidable perspective in understanding quantum criticality of a given many-body system is through its entanglement contents. Until now, most progress are only limited to the disorder-free case. Here, we develop an efficient scheme to compute the entanglement entropy of $(2+1)$-dimensional quantum critical points with randomness, from a conceptual angle where the quenched disorder can be considered as dimensionally reducible interactions. As a concrete example, we reveal novel entanglement signatures of $(2+1)$-dimensional Dirac fermion exposed to a random magnetic field, which hosts a class of emergent disordered quantum critical points. We demonstrate that the entanglement entropy satisfies the area-law scaling, and observe a modification of the area-law coefficient that points to the emergent disordered quantum criticality. Moreover, we also obtain the subleading correction to the entanglement entropy due to a finite correlation length. This subleading correction is found to be a universal function of the correlation length and disorder strength. We discuss its connection to the renormalization group flows of underlying theories.

We measured the central $(1/2\leftrightarrow -1/2)$ and first satellite $(\pm 3/2\leftrightarrow \pm 1/2)$ lines of the ${}^{139}\mathrm{La}$ NMR spectra as a function of temperature in ${\mathrm{LaAgSb}}_2$, in order to elucidate the origin and nature of the charge-density-wave (CDW) transitions at $T_{\text{CDW1}}=207\mathrm{K}$ and $T_{\text{CDW2}}=186\mathrm{K}$. In the normal state, the Knight shift $\mathcal{K}$ reveals a fairly linear relationship with decreasing temperature, which is ascribed to a pseudogap in the spin excitation spectrum, pointing towards the material being an unconventional metal. Upon further cooling, $\mathcal{K}$ decreases more steeply below $T_{\text{CDW1}}$, indicative of the partial Fermi surface gap opening on top of the pseudogap. The most remarkable finding in our study is a clear splitting of the satellite lines at $T_{\text{CDW1}}$ observed for $H\parallel c$, whose temperature dependence behaves as the BCS order parameter in the weak-coupling limit, evidencing that the CDW transition induces the periodic lattice distortion. Our NMR findings therefore demonstrate that the CDW transition in ${\mathrm{LaAgSb}}_2$ is of Peierls type, being driven by the electronic instability in the vicinity of the Fermi level.

Trimers are defined as two adjacent edges on a graph. We study the quantum states obtained as equal-weight superpositions of all trimer coverings of a lattice, with the constraint of having a trimer on each vertex: the so-called trimer resonating-valence-bond (tRVB) states. Exploiting their tensor network representation, we show that these states can host ${\mathbb{Z}}_3$ topological order or can be gapless liquids with $\mathrm{U}\left(1\right)\times \mathrm{U}\left(1\right)$ local symmetry. We prove that this continuous symmetry emerges whenever the lattice can be tripartite such that each trimer covers all the three sublattices. In the gapped case, we demonstrate the stability of topological order against dilution of maximal trimer coverings, which is relevant for realistic models where the density of trimers can fluctuate. Furthermore, we clarify the connection between gapped tRVB states and ${\mathbb{Z}}_3$ lattice gauge theories by smoothly connecting the former to the ${\mathbb{Z}}_3$ toric code, and discuss the nonlocal excitations on top of tRVB states. Finally, we analyze via exact diagonalization the zero-temperature phase diagram of a diluted trimer model on the square lattice and demonstrate that the ground state exhibits topological properties in a narrow region in parameter space. We show that a similar model can be implemented in Rydberg atom arrays exploiting the blockade effect. We investigate dynamical preparation schemes in this setup and provide a viable route for probing experimentally ${\mathbb{Z}}_3$ quantum spin liquids.

Nonlinear optical effects such as four-wave mixing and generation of squeezed light are ubiquitous in optical devices and light sources. For new devices operating at low optical power, the resonant nonlinearity arising from the two-photon sensitive bound biexciton in a semiconductor microcavity is an interesting prospective platform. Due to the particularly strong Coulomb interaction in atomically thin semiconductors, these materials have strongly bound biexcitons and operate in the visible frequency range of the electromagnetic spectrum. To remove the strong pump laser from the generated light in optical devices or to simultaneously excite nondegenerate polaritons, a bichromatic-pump configuration with two spectrally separated pump lasers is desirable. In this paper, we theoretically investigate spontaneous four-wave mixing and quadrature-squeezing in a bichromatically pumped atomically thin semiconductor microcavity. We explore two different configurations that support degenerate and nondegenerate scattering from polaritons into bound biexcitons, respectively. We find that these configurations lead to the generation of strongly single- and two-mode quadrature-squeezed light.

We study the nonlinear effect on topological edge states by including a nonlinear term to a Chern insulator which has two chiral edge states with opposite chiralities. We explore quench dynamics by giving a pulse to one site on an edge and by analyzing its time evolution. Without the nonlinearity, an initial pulse spreads symmetrically and diffuses. On the other hand, with the nonlinearity present, unexpectedly a solitonlike edge state is formed, undergoes a unidirectional propagation along the edge, and turns at a corner without backscattering or diffraction. Furthermore, its wave function is well fitted by $\propto \text{sech}\left[k_x(x-v_{x}t)\right]$. A further increase of the nonlinearity induces a self-trapping transition, where the pulse is trapped to the initial site.

The instability of magnetic states in two-dimensional magnetic materials plays a crucial role in the application of spintronics. However, the instability mechanism and magnetic state diagram of $M\text{P}{X}_3$ ($M=\mathrm{Mn}$ and Ni and $X=\mathrm{S}$ and Se) monolayer with multiple magnetic states remains elusive. In our paper, we investigate the instability of magnetic states using ab initio calculation combined with an effective Heisenberg model. We obtain a series of magnetic state diagrams of $M\text{P}{X}_3$ ($M=\mathrm{Mn}$ and Ni and $X=\mathrm{S}$ and Se) monolayer under the approaches of strain and carrier doping. We clarify the instability mechanism that is mainly determined by the nearest-neighbor exchange interaction between magnetic ions, find a higher Néel temperature in ${\mathrm{NiPSe}}_3$ monolayer, and unveil a considerable increase in hole effective mass along the armchair direction in the ${\mathrm{NiPSe}}_3$ monolayer, which leads to giant anisotropy of carrier mobility. Our results provide a useful guidance to design high-performance spintronics devices based on the $M\text{P}{X}_3$ monolayer.

The non-Hermitian skin effect, as a unique feature of non-Hermitian systems, will break the topological energy braiding of Bloch bands in open boundary systems. Going beyond the Bloch band theory, we unveil the energy braiding of non-Bloch bands by introducing a one-dimensional non-Hermitian tight-binding model. We find a generic class of topological non-Bloch bands such as the Hopf link, which is generally generated by the non-Hermitian skin effect. The energy braiding is topologically robust against any perturbations without gap closing. Furthermore, non-Bloch topological invariants are proposed based on the generalized Brillouin zone to characterize the topology of these non-Bloch bands. The topological phase transition between the distinct phases occurs with non-Bloch bands touching at exceptional points. We hope that our work can shed light on the topological energy braiding of non-Bloch bands for non-Hermitian systems.

The RKKY interaction between two impurities on a curved surface is investigated. Practical curved sample parameters are considered for investigating curvatures, similar to those observed experimentally in available samples such as graphene. For this type of two-dimensional curved system and for two types of Schrödinger and Dirac carriers, the RKKY interaction and local density of states (LDOS) are calculated. Results show that the strength of the RKKY interaction on a curved surface depends significantly on the nature of particles embedded on this surface, indicating that the geometry has a different effect on the dynamics of Schrödinger and Dirac carriers. While the curved surface increases the RKKY interaction strength for Schrödinger-type carriers in comparison with the flat sample, RKKY interaction decreases in the curved surface for Dirac-type particles. This can be understood regrading the effective magnetic field experienced by the Dirac particles as a result of the curved surface. There is also a correlation between LDOS and the RKKY interaction, which could be explained by the effect of conducting electron density on the exchange interaction mediated by these carriers.

The structural and electronic properties of an atomically-flat Te-Si(111) surface have been investigated by means of density-functional theory calculations. This system is interesting because it provides a template for the epitaxial growth of inherently 2D materials. A structural model of the surface is devised that is both energetically more favorable than the ideal on-top model proposed in the literature and dynamically stable. The model, characterized by a staggered arrangement of Te-Te dimers in the passivation layer, is a semiconductor with a narrow band gap resulting from the misalignment of the ${\mathrm{Te}}_2$ units. As for the on-top case, however, this structure does not fully conforms to the available experimental observations. A finite-temperature model is hence prepared by means of molecular dynamics simulations at 300 K. It turns out that such a model is characterized by a disordered passivation layer consisting of randomly oriented ${\mathrm{Te}}_2$ units and Te chains, which makes it effectively compliant with all the experimental structural data at hand. In addition, it is also a narrow-gap semiconductor compatible with the electrical conductance measurements. These findings suggest that this model is a good candidate for representing the Te-Si(111) surface.

The electronic structure of a two-dimensional ferromagnetic $\mathrm{Mn}{\mathrm{Se}}_2$ monolayer was investigated using density functional theory. It was found that the computed Curie temperature ($T_{\mathrm{C}}$), which is fairly high but lower than room temperature, is sensitive to the on-site Coulomb repulsion $U$, indicating that electronic correlations have an important role in the magnetism exhibited in the system. The primary exchange mechanism responsible for the large $T_{\mathrm{C}}$ of monolayer $\mathrm{Mn}{\mathrm{Se}}_2$ was also clarified. Furthermore, it was demonstrated that the $T_{\mathrm{C}}$ can be enhanced up to nearly room temperature through charge doping and heterostructure engineering. These findings not only provide a fundamental understanding of the mechanism of magnetic ordering in $\mathrm{Mn}{\mathrm{Se}}_2$ monolayers, but also suggest a practical remedy for the enhancement of the $T_{\mathrm{C}}$ of $\mathrm{Mn}{\mathrm{Se}}_2$ by using various substrates, including Dirac materials.

We uncover the pressure variation of electronic states of the single-component molecular material $\mathrm{Pd}{\left(\mathrm{tmdt}\right)}_2$ that hosts the antiferromagnetic (AFM) Mott insulator at ambient pressure, using ${}^{13}\mathrm{C}$ nuclear magnetic resonance (NMR) spectroscopy. Under pressures up to 8.5 kbar, the NMR spectral broadening and the peak structure in the temperature dependence of the spin-lattice relaxation rate $1\text{/}{T}_1$ are observed and indicate that the AFM transition persists in this pressure range. However, the Neel temperature and the AFM magnetic moment are continuously decreased toward a critical pressure of $\sim 9$ kbar. At 10 kbar, these AFM features in the spectra and $1\text{/}{T}_1$ are suppressed, and instead $1\text{/}{T}_{1}T$ exhibits a critical increase toward zero temperature, complying with the self-consistent renormalization (SCR) theory in two-dimensional AFM itinerant magnets [$1\text{/}{T}_{1}T$ $\sim$ (${T+\theta )}^{-1}$], which also explains the systematic change of $1\text{/}{T}_{1}T$ at higher pressures. The present results indicate that $\mathrm{Pd}{\left(\mathrm{tmdt}\right)}_2$ shows a pressure-induced quantum phase transition from the AFM Mott insulator to the paramagnetic metal at the quantum critical point of $\sim 9$ kbar.

Quantum many-body scar states are special eigenstates of nonintegrable models with distinctive entanglement features that give rise to infinitely long-lived coherent dynamics under quantum quenches from certain initial states. We elaborate on a construction of quantum many-body scar states in which they emerge from Einstein-Podolsky-Rosen states in systems with two layers, wherein the two layers are maximally entangled. We apply this construction to spin systems as well as systems of itinerant fermions and bosons and demonstrate how symmetries can be harnessed to enhance its versatility. We show that several well-known examples of quantum many-body scars, including the tower of states in the spin-1 $XY$ model and the $\eta$-pairing states in the Fermi-Hubbard model, can be understood within this formalism. We also demonstrate how an infinite tower of many-body scar states can emerge in bilayer Bose-Hubbard models with charge conservation.

Substituting magnetic ions with nonmagnetic ions is a new way to study dilution. Using determinant quantum Monte Carlo calculations, we investigate an interacting Dirac fermion model with the onsite Coulomb repulsion being randomly zero on a fraction $x$ of sites. Based on conductivity, density of states, and antiferromagnetic structure factor, our results reveal a novel intermediate insulating phase induced by the competition between dilution and repulsion. With increasing doping level of nonmagnetic ions, this nonmagnetic intermediate phase is found to emerge from the zero-temperature quantum critical point separating a metallic and a Mott insulating phase, whose robustness is proven over a wide range of interactions. Under the premise of strongly correlated materials, we suggest that doping nonmagnetic ions can effectively convert the system back to the paramagnetic metallic phase. This result not only agrees with experiments on the effect of dilution on magnetic order but also provides a possible direction for studies focusing on the metal-insulator transition in honeycomb lattice-like materials.