Unidirectional transport and localized cyclotron motion are two opposite physical phenomena. Here, we study the interplay effects between them on nonreciprocal lattices subject to a magnetic field. We show that, in the long-wavelength limit, the trajectories of the wave packets always form closed orbits in four-dimensional complex space. Therefore, the semiclassical quantization rules persist despite the nonreciprocity, which preserves real Landau levels. We predict a different type of non-Hermitian spectral transition induced by the spontaneous breaking of the combined mirror-time reversal ($\mathcal{MT}$) symmetry, which generally exists in such systems. An order parameter is proposed to describe the $\mathcal{MT}$ phase transition, not only to determine the $\mathcal{MT}$ phase boundary but also to quantify the degree of $\mathcal{MT}$-symmetry breaking. Such an order parameter can be generally applied to all types of non-Hermitian phase transitions.

Many-body localization (MBL) is a novel prototype of ergodicity breaking due to the emergence of local integrals of motion (LIOMs) in a disordered interacting quantum system. To better understand the role played by the existence of such LIOMs, we explore and study some of their structural properties across the MBL transition. We first consider a one-dimensional XXZ spin chain in a disordered magnetic field and introduce and implement a nonperturbative, fast, and accurate method of constructing LIOMs. In contrast to already existing methods, our scheme allows obtaining LIOMs not only in the deep MBL phase but, rather, near the transition point too. Then, we take the matrix representation of LIOM operators as an adjacency matrix of a directed graph whose elements describe the connectivity of ordered eigenbasis in the Hilbert space. Our cluster-size analysis for this graph shows that the MBL transition coincides with a percolation transition in the Hilbert space. By performing finite-size scaling, we compare the critical disorder and correlation exponent $\nu$ both in the presence and absence of interactions. Finally, we also discuss how the distribution of diagonal elements of LIOM operators in a typical cluster signals the transition.

The interplay between magnetism and topological band structure offers extraordinary opportunities to realize rich exotic magnetic topological phases such as axion insulators, Weyl semimetals, and quantum anomalous Hall insulators, and therefore has attracted fast growing research interest. The rare-earth hexaboride $\mathrm{Eu}{\mathrm{B}}_6$ represents an interesting magnetic topological phase with tunable magnetizations along different crystallographic directions, while the correlation with the topological properties remains scarcely explored. In this work, combining magnetotransport measurements and first principles calculations, we demonstrate that $\mathrm{Eu}{\mathrm{B}}_6$ exhibits versatile magnetic topological phases along different crystallographic directions, which tightly correlate with the varied magnetizations. Moreover, by virtue of the weak magnetocrystalline anisotropy and the relatively strong coupling between the local magnetization and the conduction electrons, we show that the magnetic ground state of the system can be directly probed by the anisotropy in the magnetotransport properties. Our work thus introduces an excellent platform to study the rich topological phases that are tunable by magnetic orders.

We have investigated magnetoelectric (ME) coupling in the single-molecule magnet ${\mathrm{Mn}}_4{\mathrm{Te}}_4{\left(\mathrm{P}{\mathrm{Et}}_3\right)}_4$ with tetrahedral spin frustration. Our density functional studies found that an electric dipole moment can emerge with various noncollinear spin orderings. The forms of spin-dependent dipole are determined and consistent with that in noncentrosymmetric magnets driven by the Dzyaloshinskii-Moriya interaction. Writing a parameterized spin Hamiltonian, after solving for eigenvalues and eigenstates, we quantified the ME coupling by calculating the thermal average of the electric and magnetic susceptibilities, which can be influenced by external magnetic and electric fields, respectively. The quadratic relations are expected to be observable in experiments.

We carry out a systematical study of the size scaling of the Liouvillian gap in boundary-dissipated one-dimensional quasiperiodic and disorder systems. By treating the boundary-dissipation operators as a perturbation, we derive an analytical expression of the Liouvillian gap, which indicates clearly the Liouvillian gap being proportional to the minimum of boundary densities of eigenstates of the underlying Hamiltonian, and thus give a theoretical explanation why the Liouvillian gap has different size scaling relation in the extended and localized phase. While the Liouvillian gap displays a power-law size scaling ${\mathrm{\Delta }}_g\propto L^{-3}$ in the extended phase, our analytical result unveils that the Liouvillian gap fulfills an exponential scaling relation ${\mathrm{\Delta }}_g\propto e^{-\kappa L}$ in the localized phase, where $\kappa$ takes the largest Lyapunov exponent of localized eigenstates of the underlying Hamiltonian. By scrutinizing the extended Aubry-André-Harper model, we numerically confirm that the Liouvillian gap fulfills the exponential scaling relation and the fitting exponent $\kappa$ coincides pretty well with the analytical result of the Lyapunov exponent. The exponential scaling relation is further verified numerically in other one-dimensional quasiperiodic and random disorder models. We also study the relaxation dynamics and show the inverse of the Liouvillian gap giving a reasonable timescale of asymptotic convergence to the steady state.

This work presents micromagnetic simulations in ferromagnetic nanogratings for the full range of directions of an applied in-plane external magnetic field. We focus on the modification of the magnon mode characteristics when the magnetic field orientation is gradually changed between the classical Damon-Eshbach and backward-volume geometries. We found that in a specific range of field directions, the magnon mode parameters differ significantly from the parameters in the classical cases; namely, the modes are characterized by complex spatial distributions and have low group velocities. The center of this range corresponds to the direction of the external magnetic field, which gives the maximal nonuniform distribution of the static magnetization in the nanogratings.

We theoretically investigate a $J_1\text{−}{J}_3$ classical Heisenberg model on the breathing pyrochlore lattice, where the nearest-neighbor (NN) exchange interactions for small and large tetrahedra, $J_1$ and $J_1^{\prime }$, take different values due to the breathing bond alternation and $J_3$ is the third NN antiferromagnetic interaction along the bond direction. It is found by means of Monte Carlo simulations that for large $J_3$, a hedgehog lattice, a three-dimensional periodic array of magnetic monopoles and antimonopoles, emerges in the form of a quadruple-$\mathbf{Q}$ state characterized by the ordering vector of $\mathbf{Q}=(\pm \frac{1}{2},\pm \frac{1}{2},\pm \frac{1}{2})$, being irrespective of the signs of $J_1$ and/or $J_1^{\prime }$ as long as $J_1\ne J_1^{\prime }$. It is also found that in an applied magnetic field, there appear six quadruple-$\mathbf{Q}$ states depending on the values of $J_1$ and $J_1^{\prime }$, among which three phases including the in-field hedgehog-lattice state exhibit nonzero total chirality ${\mathit{\chi }}^{\mathrm{T}}$ associated with the anomalous Hall effect of chirality origin. In the remaining two chiral phases, which are realized in the presence of ferromagnetic $J_1$ and/or $J_1^{\prime }$, the spin structure is not topologically nontrivial, in spite of the fact that ${\mathit{\chi }}^{\mathrm{T}}\ne 0$. The role of the topological objects of the monopoles in ${\mathit{\chi }}^{\mathrm{T}}$ is also discussed.

By using the extended Hubbard model of anyons, we numerically demonstrate the adiabatic deformation of the spinful quantum Hall (QH) states by transmutation of statistical fluxes. While the ground state is always spin-polarized in a series of $\nu =1$ integer QH systems, the adiabatic continuity between the singlet QH states at $\nu =2$ and $\nu =2/5$ is confirmed. These results are consistent with the composite fermion theory with spin. The many-body Chern number of the ground-state multiplet works as an adiabatic invariant and also explains the discrete change of the topological degeneracy during the evolution. The generalized Středa formula of spinful systems is justified.

The incommensurate twist structure and the interlayer coupling induce van der Waals quasicrystals (vdW-QCs). Replacing conventional band theory requiring translational symmetry, the resonant coupling Hamiltonian endowing the quasiband structure in $\mathit{k}$ space is adopted to describe electronic properties of vdW-QCs [Moon et al., Phys. Rev. B 99, 165430 (2019)]. Here we investigate the symmetries of the resonant coupling Hamiltonians in dodecagonal and octagonal vdW-QCs. Through symmetry analyses we derive compatibility relationships (CRs) between $\mathrm{\Gamma }$ point and other irreducible pathways and predict the symmetry changes and band splits. Especially, we find that from $\mathrm{\Gamma }$ point to Brillouin zone corner points of monolayers, arbitrary twofold degenerate states are split into one $A^{\prime }$ and one $A^{″}$ state, and from $\mathrm{\Gamma }$ point to the intersection points of two Brillouin zones of monolayers, arbitrary twofold degenerate states are split into one $A$ and one $B$ state. Instead of projection operation analyses, we discuss the CRs of different point groups between the coupled bilayers and uncoupled monolayers to construct the interlayer hybridization selection rules (IHSRs) [Yu et al., Phys. Rev. B 105, 125403 (2022)], which govern how the interlayer states interact with each other in the resonant coupling systems of dodecagonal and octagonal vdW-QCs. These derived IHSRs indicate that the first two main resonant couplings allow the nonequivalent hybridizations only between $B_1$ and $B_2$ states and the equivalent hybridizations for $A$, $A_i$, $A^{\prime }$, $A^{″}$, $E$, or $E_i$ states.

Over the years, many theoretical frameworks have been developed to understand the remarkable physics of the quantum Hall system. In this work we discuss the interplay among quantum wires, Chern-Simons theory, bosonization, and particle-vortex duality, which enable a unified approach for the Laughlin states of the fractional quantum Hall system. Starting from the so-called quantum wires system, which is a semimicroscopic description in terms of $(1+1)$-dimensional theories, we discuss the emergence of $(2+1)$-dimensional low-energy effective field theories by using different maps connecting the microscopic degrees of freedom with the macroscopic ones. We show the origin of these maps by embedding the bosonized version of the original quantum wires model in a gauge-invariant theory and using particle vortex duality.

Local moment formation is ubiquitous in disordered semiconductors such as Si:P, where it is observed both in the metallic and the insulating regimes. Here, we focus on local moment behavior in disordered insulators, which arises from short-ranged, repulsive electron-electron interactions. Using density matrix renormalization group and strong-disorder renormalization group methods, we study paradigmatic models of interacting insulators: one-dimensional Hubbard chains with quenched randomness. In chains with either random fermion hoppings or random chemical potentials, both at and away from half-filling, we find exponential decay of disorder-averaged charge and fermion two-point correlations, but power-law decay of disorder-averaged spin correlations that are indicative of the random singlet phase. The numerical results can be understood qualitatively by appealing to the large-interaction limit of the Hubbard chain, in which a remarkably simple picture emerges.

The charged exciton recombination and their spin dynamics are studied in ultrathin InSb- and AlSb-based quantum wells (QWs) surrounded by an AlAs matrix characterized by an indirect band gap. Strong material intermixing was observed that results in the QWs being composed of a quaternary ${\mathrm{In}}_x{\mathrm{Al}}_{1-x}{\mathrm{Sb}}_y{\mathrm{As}}_{1-y}$ or a ternary ${\mathrm{AlSb}}_y{\mathrm{As}}_{1-y}$ alloy. The band alignment in these QWs is identified as type I for (In,Al)(Sb,As)/AlAs and type II for Al(Sb,As)/AlAs. The magnetic-field-induced circular polarization of the photoluminescence $P_c$ is studied as function of the field strength. The observed nonmonotonic behavior of the $P_c$ dynamics at high magnetic fields is provided by the interplay of negative and positive trions, contributing to the emission. To interpret the experiment, we have developed a kinetic equation model which accounts for the dynamics of the trion spin states and the redistribution of trions between these states as a result of spin relaxation. The model is in quantitative agreement with the experiment and allows us to determine trion radiative lifetimes on the order of hundreds of microseconds, holes in the trion spin-relaxation times also in the hundreds of $\mu \mathrm{s}$ range, electrons in the trion spin-relaxation times of hundreds of ns, and heavy-hole $g$ factors of about $+3.5$ for the structures studied.

The spin-dependent band structure of ${\mathrm{CoS}}_2$, which is a candidate for a half-metallic ferromagnet, was investigated by both spin- and angle-resolved photoemission spectroscopy and theoretical calculations to reappraise the half-metallicity and electronic correlations. We determined the three-dimensional Fermi surface and the spin-dependent band structure. As a result, we found that a part of the minority spin bands is on the occupied side in the vicinity of the Fermi level, providing spectroscopic evidence that ${\mathrm{CoS}}_2$ is not a half-metal but very close. Band calculations using density functional theory with generalized gradient approximation showed good agreement with the observed majority spin $e_g$ bands, while it could not explain the observed band width of the minority-spin $e_g$ bands. On the other hand, theoretical calculations using dynamical mean field theory could better reproduce the strong mass renormalization in the minority-spin $e_g$ bands. Our results strongly suggest the presence of anomalously enhanced spin-dependent electron correlation effects on the electronic structure in the vicinity of the half-metallic state. We also report the temperature dependence of the electronic structure across the Curie temperature and discuss the mechanism of the thermal demagnetization. Our discovery of the anomalously large spin-dependent electronic correlations not only demonstrates a key factor in understanding the electronic structure of half-metals but also provides a motivation to improve theoretical calculations on spin-polarized strongly correlated systems.

The family of rare-earth chalcogenides $A{\mathrm{RECh}}_2$ ($A$ = alkali or monovalent ions, RE = rare earth, and Ch = O, S, Se, and Te) appears as an inspiring playground for studying quantum spin liquids (QSLs). The crucial low-energy spin dynamics remain to be uncovered. By employing muon spin relaxation ($\mu \mathrm{SR}$) and zero-field (ZF) AC susceptibility down to 50 mK, we are able to identify the gapless QSL in ${\mathrm{NaYbSe}}_2$, a representative member with an effective spin-1/2, and explore its unusual spin dynamics. The ZF $\mu \mathrm{SR}$ experiments unambiguously rule out spin ordering or freezing in ${\mathrm{NaYbSe}}_2$ down to 50 mK, which is two orders of magnitude smaller than the exchange coupling energies. The spin relaxation rate $\lambda$ approaches a constant below 0.3 K, indicating that finite spin excitations are featured by a gapless QSL ground state. This is consistently supported by our AC susceptibility measurements. The careful analysis of the longitudinal field (LF) $\mu \mathrm{SR}$ spectra reveals a strong spatial correlation and a temporal correlation in the spin-disordered ground state, highlighting the unique feature of spin entanglement in the QSL state. The observations allow us to establish an experimental H-T phase diagram. The study offers insight into the rich and exotic magnetism of the rare-earth family.

We report the crystallographic and electrical transport properties of single crystals of the ferromagnetic two-dimensional (2D) material ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$ under high pressure. In contrast to previous studies, our high-pressure single-crystal x-ray diffraction under hydrostatic conditions shows prominent anisotropic compressibility in the layered structure of the crystalline $R\overline{3}$ phase of ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$ without any structural phase transitions up to 20 GPa. Our data confirm a distinct and irreversible crystalline-amorphous transformation in ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$. The loss of crystallinity starts at 20 GPa; however, the crystalline phase and amorphous state coexist even at the maximum pressure of 31.2 GPa. High-pressure powder x-ray diffraction data and electrical resistivity measurements of ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$ using NaCl as the pressure-transmitting medium reveal an insulator-to-metal transition in the absence of a phase transition at ∼3.9 GPa; at a considerably lower pressure than the previously reported (7–14 GPa). Density functional theory calculations demonstrate the density of states around the Fermi level are primarily dominated by Cr $3d$ and Te $5p$ states. Hence the large reduction of Cr-Te bond lengths within the ${\mathrm{CrTe}}_6$ octahedra under compression is most likely responsible for the band-gap closure. This study clarifies that the phase stability and onset of metallization pressure in the ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$ sample are sensitive to the hydrostatic environments and demonstrates how pressure can be used to tune the physical properties of 2D ferromagnetic compounds.

Experimental realizations of topologically ordered states of matter, such as fractional quantum Hall states, with cold atoms are now within reach. In particular, optical lattices provide a promising platform for the realization and characterization of such states, where novel detection schemes enable an unprecedented microscopic understanding. Here we show that the central charge can be directly measured in current cold atom experiments using the number entropy as a proxy for the entanglement entropy. We perform density-matrix renormalization-group simulations of Hubbard-interacting bosons on coupled chains subject to a magnetic field with $\alpha =1/4$ flux quanta per plaquette. Tuning the interchain hopping, we find a transition from a trivial quasi-one-dimensional phase to the topologically ordered Laughlin state at magnetic filling factor $\nu =1/2$ for systems of three or more chains. We resolve the transition using the central charge, on-site correlations, momentum distributions, and the many-body Chern number. Additionally, we propose a scheme to experimentally estimate the central charge from Fock basis snapshots. The model studied here is experimentally realizable with existing cold atom techniques and the proposed observables pave the way for the detection and classification of a larger class of interacting topological states of matter.

A quantum spin impurity coupled to a gapless free field (the Bose-Kondo model) can be represented as a $(0+1)$-dimensional field theory with long-range-in-time interactions that decay as $|t-t^{\prime }{|}^{-(2-\delta )}$. This theory is a simpler analog of nonlinear $\sigma$ models with topological Wess-Zumino-Witten terms in higher dimensions. In this Letter we show that the renormalization group (RG) flows for the impurity problem exhibit an annihilation between two nontrivial RG fixed points at a critical value ${\delta }_c$ of the interaction exponent. The calculation is controlled at large spin $S$. This clarifies the phase diagram of the Bose-Kondo model and shows that it serves as a toy model for phenomena involving fixed point annihilation and “quasiuniversality” in higher dimensions.

We present a theoretical model of composite excitonic states in doped semiconductors. Many-body interactions between a photoexcited electron-hole pair and the electron gas are integrated into a computationally tractable few-body problem, solved by the variational method. We focus on electron-doped monolayer (ML)-$\mathrm{Mo}{\mathrm{Se}}_2$ and ML-$\mathrm{W}{\mathrm{Se}}_2$ due to the contrasting character of their conduction bands. In both cases, the core of the composite is a tightly bound trion (two electrons and a valence-band hole) surrounded by a region depleted of electrons. The composite in ML-$\mathrm{W}{\mathrm{Se}}_2$ further includes a satellite electron with different quantum numbers. The theory is general and can be applied to semiconductors with various energy-band properties, allowing one to calculate their excitonic states and to quantify the interaction with the Fermi sea.

Liquid deuterium is a fluid between the quantum and classical regimes. It attracts interest from fundamental research for the verification of quantum calculations but also from neutron physics as it is a widely used neutron moderator medium. We have measured the scattering cross sections of liquid ortho-deuterium in the ultracold-neutron range for four different temperatures (19–23 K) and compared them with calculations from a parameter-free analytical calculation model as well as with previous measurements at 19 K by another research group. All three show remarkable agreement, which establishes the validity of the calculation model and proves it is a reliable basis for the derivation of scattering kernels. The deconvolution of our measured transmission data changed the cross-section results noticeably only for neutrons faster than 10 m/s. We found the total scattering cross section of liquid deuterium to be inversely proportional to velocity, as is predicted by theory.