We study the angular-time evolution that is a parameter-time evolution defined by the entanglement Hamiltonian for the bipartitioned ground state of the Affleck-Kennedy-Lieb-Tasaki (AKLT) chain with an open boundary. In particular, we analytically calculate angular-time spin correlation functions $\langle S_n^{\alpha }\left(\tau \right)S_n^{\alpha }\left(0\right)\rangle$ with $\alpha =x,y,z$ using the matrix-product-state (MPS) representation of the valence-bond-solid state with edges. We also investigate how the angular-time evolution operator can be represented in the physical spin space with the use of gauge transformation for the MPS. We then discuss the physical interpretation of the angular-time evolution in the AKLT chain.

Magnetization relaxation in the two-dimensional itinerant ferromagnetic van der Waals material ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$, below the Curie temperature, is fundamentally important for applications to low-dimensional spintronics devices. We use first-principles scattering theory to calculate the temperature-dependent Gilbert damping for bulk and single-layer ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$. The calculated damping frequency of bulk ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$ increases monotonically with temperature because of the dominance of resistivitylike behavior. By contrast, a very weak temperature dependence is found for the damping frequency of a single layer, which is attributed to strong surface scattering in this highly confined geometry. A systematic study of the damping anisotropy reveals that orientational anisotropy is present in both bulk and single-layer ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$. Rotational anisotropy is significant at low temperatures for both the bulk and a single layer and is gradually diminished by temperature-induced disorder. The rotational anisotropy can be significantly enhanced by up to 430% in gated single- layer ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$.

We study the two-dimensional Rydberg atom array in an optical cavity with the help of a variational method and large-scale quantum Monte Carlo simulations. The strong dipole-dipole interactions between Rydberg atoms can make the system exhibit a crystal structure, and the coupling between a two-level atom and a cavity photon mode can result in the formation of a polariton. The interplay between them provides a rich quantum phase diagram including the Mott, solid-1/2, superradiant, and superradiant solid (SRS) phases. As a two-order coexisted phase, the superradiant solid breaks both translational and U(1) symmetries. Different from the fragile SRS phase in a one-dimensional system [Zhang et al., Phys. Rev. Lett. 110, 090402 (2013)], the SRS phase stays in a larger parameter region. Thus, it is more feasible to detect a SRS phase and corresponding quantum criticality in the real system involving dissipations. Our work not only extends the understanding of the light-atom interacting system, but also provides the guidelines and benchmark for the future experiments.

We investigated magnetic vortices in two stoichiometric LiFeAs samples by means of scanning tunneling microscopy and spectroscopy. The vortices were revealed by measuring the local electronic density of states at zero bias conductance of samples in magnetic fields between 0.5 and 12 T. From single vortex spectroscopy we extract the Ginzburg-Landau coherence length of both samples as $4.4\pm 0.5$ nm and $4.1\pm 0.5$ nm, in accordance with previous findings. However, in contrast to previous reports, our study reveals that the reported hexagonal-to-squarelike vortex lattice transition is absent up to 12 T both in field-cooling and zero-field-cooling processes. Remarkably, a highly ordered zero-field-cooled hexagonal vortex lattice is observed up to 8 T. We argue that several factors are likely to determine the structure of the vortex lattice in LiFeAs such as (i) details of the cooling procedure, (ii) sample stoichiometry that alters the formation of nematic fluctuations, (iii) details of the order parameter, and (iv) magnetoelastic coupling.

We introduce a class of spinless fermion models that exhibit quantum many-body scars (QMBS) originating from kinetic constraints in the form of density-assisted hopping. The models can be defined on any lattice in any dimension and allow for spatially varying interactions. We construct a tower of exact eigenstates with finite energy density, and we demonstrate that these QMBS are responsible for the nonthermal nature of the system by studying the entanglement entropy and correlation functions. The quench dynamics from certain initial states is also investigated, and it is confirmed that the QMBS induce nonthermalizing dynamics. As another characterization of the QMBS, we give a parent Hamiltonian for which the QMBS are unique ground states. We also prove the uniqueness rigorously.

Erbium doped crystals offer a versatile platform for hybrid quantum devices because they combine magnetically sensitive electron-spin transitions with telecom-wavelength optical transitions. At the high doping concentrations necessary for many quantum applications, however, strong magnetic interactions of the electron-spin bath lead to excess spectral diffusion and rapid decoherence. Here we lithographically fabricate a 4.4 GHz superconducting planar microresonator on a ${\text{CaWO}}_4$ crystal doped with Er ions at a concentration of 20 ppm relative to Ca. Using the microwave resonator, we characterize the spectral diffusion processes that limit the electron-spin coherence of Er ions at millikelvin temperatures by applying two- and three-pulse echo sequences. The coherence time shows a strong temperature dependence, reaching 1.3 ms at 23 mK for an electron-spin transition of ${}^{167}\mathrm{Er}$.

Aharonov-Bohm caging is a localization mechanism stemming from the competition between the geometry and the magnetic field. Originally described for a tight-binding model in the dice lattice, this destructive interference phenomenon prevents any wavepacket spreading away from a strictly confined region. Accordingly, for the peculiar values of the field responsible for this effect, the energy spectrum consists of a discrete set of highly degenerate flat bands. In the present work, we show that Aharonov-Bohm cages are also found in an infinite set of hyperbolic dice tilings defined on a negatively curved hyperbolic plane. We detail the construction of these tilings and compute their Hofstadter butterflies by considering periodic boundary conditions on high-genus surfaces. As recently observed for some regular hyperbolic tilings, these butterflies do not manifest the self-similar structure of their Euclidean counterparts but still contain some gaps. We also consider the energy spectrum of hyperbolic kagome tilings (which are the dual of hyperbolic dice tilings), which displays interesting features, such as highly degenerate states arising for some particular values of the magnetic field. For these two families of hyperbolic tilings, we compute the Chern number in the main gaps of the Hofstadter butterfly and propose a gap labeling inspired by the Euclidean case. Finally, we also study the triangular Husimi cactus, which is a limiting case in the family of hyperbolic kagome tilings, and we derive an exact expression for its spectrum versus magnetic flux.

A twisted light is a spatially structured light that carries quantized orbital angular momenta (OAM), being a new degree of freedom useful in quantum information technology in addition to that of intrinsic spin angular momentum (SAM), i.e., polarization. Using polarized twisted light to excite valley excitons in transition-metal dichalcogenide monolayers (TMD-ML's) sets up an intriguing photoexcited system which couples comprehensively the excitonic and photonic multi-degrees of freedom, including the center-of-mass motion and valley polarization of exciton and the both optical OAM and SAM. In this work, we present a systematic theoretical investigation of the photoexcited valley excitons in TMD-ML's by polarized Laguerre-Gaussian beams, one of the best known twisted light (TL). We show that the photoexcitation of polarized TL incident to a TMD-ML leads to the formation of the superposition of finite-momentum exciton (SFME) states, spatially localized with the OAM- and SAM-encoded geometrical patterns.

Using ab initio band structure methods and $\mathrm{DFT}+$dynamical mean-field theory approach we explore the possible formation of spin and charge stripes in the Ni–O plane of hole-doped infinite-layer nickelates, $R{\mathrm{NiO}}_2$. Our results reveal a remarkable instability of the $C$-type $\left(110\right)$ spin state with undistorted lattice towards the formation of the spin density, charge and bond disproportionation stripe phases accompanied by in-plane“breathinglike” distortions of the crystal structure. Our work gives a comprehensive picture of competing charge and spin stripe states, with possible frustration of different stripe patterns upon doping. It suggests that the spin and charge stripe state likely arises from strong magnetic correlations (with concomitant lattice distortions), which play a key role for understanding the anomalous properties of hole-doped layered nickelates.

We extend the $p_x-p_y$ large-gap scenario to the band inversion systems and exemplify the mechanism with a family of III-Bi honeycomb monolayers on $\mathrm{Si}{\mathrm{O}}_2$, which can be the next generation of large-gap quantum spin Hall (QSH) systems. First, it suggests a topological gap of the same order as the current record kept of bismuthene/SiC(0001). Second, the band inversion mechanism in which these QSH insulators originate is qualitatively distinct from the Kane-Mele paradigm. Our work demonstrates that the $p_x\text{−}{p}_y$ scenario can be utilized to promote large-gap QSH states with both Kane-Mele and band inversion mechanisms, providing an efficient building principle for future topological device construction.

We perform a comparative study for the magnetization dynamics within linear response theory of one and two dimensional massive Dirac electrons, after switching on either a real (Hermitian) or an imaginary (non-Hermitian) magnetic field. While Hermitian dc magnetic fields polarize the spins in the direction of the external magnetic field, non-Hermitian magnetic fields induce only off diagonal response. An imaginary dc magnetic field perpendicular to the mass term induces finite magnetization in the third direction only according to the right hand rule. This can be understood by analyzing the non-Hermitian equation of motion of the spin, which becomes analogous to a classical particle in crossed electric and magnetic fields. Therein, the spin expectation value, the mass term, and imaginary magnetic field play the role of the classical momentum, magnetic, and electric field, respectively. The latter two create a drift velocity perpendicular to them, which gives rise to the off-diagonal component of the dc spin susceptibility, similarly to how the Hall effect develops in the classical description.

The crossing of a continuous phase transition results in the formation of topological defects with a density predicted by the Kibble-Zurek mechanism (KZM). We characterize the spatial distribution of pointlike topological defects in the resulting nonequilibrium state and model it using a Poisson point process in arbitrary spatial dimensions with KZM density. Numerical simulations in a one-dimensional ${\varphi }^4$ theory unveil short-distance defect-defect corrections stemming from the kink excluded volume, while in two spatial dimensions, our model accurately describes the vortex spacing distribution in a strongly coupled superconductor indicating the suppression of defect-defect spatial correlations.

Multiple intriguing phenomena have recently been discovered in tetragonal Heusler compounds, where $D_{2d}$ symmetry sets a unique interplay between Dzyaloshinskii-Moriya (DM) and magnetic dipolar interactions. In the prototype $D_{2d}$ compound ${\mathrm{Mn}}_{1.4}\mathrm{PtSn}$, this has allowed the stabilization of exotic spin textures, such as first-reported antiskyrmions or elliptic Bloch-type skyrmions. Although less attention has so far been given to the low-field spiral state, this remains extremely interesting as a simplest phase scenario on which to investigate the complex hierarchy of magnetic interactions in this materials family. Here, via resonant small-angle soft x-ray scattering experiments on high-quality single crystals of ${\mathrm{Mn}}_{1.4}\mathrm{PtSn}$ at low temperatures, we evidence how the underlying $D_{2d}$ symmetry of the DM interaction in this material is reflected in its magnetic texture. Our studies reveal the existence of a novel and complex metastable phase, which possibly has a mixed character of both the Néel-type cycloid and the Bloch-type helix, that forms at low temperature in zero fields upon the in-plane field training. This hybrid spin-spiral structure has a remarkable tunability, allowing to tilt its orientation beyond high-symmetry crystallographic directions and control its spiral period. These results broaden the richness of the exotic magnetic phase diagram of Heusler $D_{2d}$ materials and extend their tunability, thus, enhancing a relevant playground for further fundamental explorations and potential applications in energy-saving technologies.

The discovery of nonlocal order parameters in real space provides a feasible scheme for studying dynamical critical behavior in topological systems. We study the critical phenomena in the one-dimensional Su-Schrieffer-Heeger (SSH) model by investigating the inhomogeneities in the local winding number in real space. By slowly quenching the system across the topological phase transition during a finite time interval, we find that the length scale defined through the local winding number satisfies the Kibble-Zurek mechanism. In contrast to the density of excitation, the scaling of this length scale is in full analog to the behavior of traditional continuous phase transitions with local order parameter and spontaneous symmetry breaking. In addition, the critical behavior and Kibble-Zurek mechanism in the generalized SSH with next-nearest-neighbor hopping are also studied. These results extend our understanding to the Kibble-Zurek mechanism and topological phase transition in nonequilibrium.

In a scenario of spontaneous symmetry breaking in finite time, topological defects are generated at a density that scales with the driving time according to the Kibble-Zurek mechanism (KZM). Signatures of universality beyond the KZM have recently been unveiled: The number distribution of topological defects has been shown to follow a binomial distribution, in which all cumulants inherit the universal power-law scaling with the quench rate, with cumulant rations being constant. In this work, we analyze the role of boundary conditions in the statistics of topological defects. In particular, we consider a lattice system with nearest-neighbor interactions subject to soft antiperiodic, open, and periodic boundary conditions implemented by an energy penalty term. We show that for fast and moderate quenches, the cumulants of the kink number distribution present a universal scaling with the quench rate that is independent of the boundary conditions except for an additive term, which becomes prominent in the limit of slow quenches, leading to the breaking of power-law behavior. We test our theoretical predictions with a one-dimensional scalar theory on a lattice.

Describing the (a) electronic and magnetic properties (EMPs) of compounds generally requires the specification of (b) the type of spin configurations one is considering [e.g., antiferromagnetic (AFM) or paramagnetic (PM) phases, with or without spin short-range order (SRO)] and lattice structure (e.g., atomic displacements, possible symmetry breaking) of such phases at a given temperature. Indeed, studying the interplay between the spin configuration and lattice structure (SCLS) and the ensuing EMPs has been an outstanding challenge in the theory of matter. The traditional approach of electronic phases of matter has generally focused on the interelectronic interactions, regarding the lattice structure as a spectator degree of freedom (DOF), often fixed from an external source (experiment or model assumptions). However, one expects that the EMPs of a compound can generally respond self-consistently to changes in SCLS (including symmetry), and at the same time, the SCLS can change in response to different electron and spin distributions visited during the calculation of the EMPs. This ping-pong-like interplay where structure affects electronic properties and the latter affect structure is indeed a cornerstone of much of the intricacy of understanding quantum materials. However, there is a limited understanding of the theory required to determine the SCLS at finite temperature in a way that can affect the EMPs and vice versa. We use here a practical, density functional theory (DFT)-based approach that provides the SCLS as a function of temperature, involving the description of spin, lattice, and spin-lattice dynamics of AFM and PM phases, thus providing the required ping-pong partners to the description of the EMPs of different phases. We distinguish three levels of dynamics: (I) dynamics of the spin DOFs treated via noncollinear Heisenberg Monte Carlo solved with exchange energies obtained from first-principles DFT cluster expansion, (II) dynamics of the lattice DOFs treated by ab initio molecular dynamics (AIMD) employing a fixed, representative spin configuration from Level I at the simulated temperature, and (III) coupling of spin and lattice dynamics via Landau-Lifshitz-Gilbert spin dynamics combined with AIMD. Such SCLSs at each of the three levels are used as inputs to DFT supercell calculations, providing the EMPs at each temperature. The results of this sequence include electronic band structures, bandgaps, density of states, as well as the statistical distribution of local moments and the SRO parameters, each as a function of temperature. Herein, we define a path to include temperature in magnetic insulators at different levels of spin dynamics by intercommunication between electronic structure theory and statistical mechanics. Using NiO as a test case, we address the separability of the DOFs in magnetic insulators for a minimal description of EMPs, demonstrating that inclusion of spin dynamics and, to some level, lattice dynamics is enough to explain the EMPs.

Using quantum Monte Carlo simulations, we study the spin-1/2 Heisenberg model on a two-dimensional lattice formed by coupling diagonal ladders. The model hosts an antiferromagnetic Néel phase, a rung singlet product phase, and a topological nontrivial Haldane phase, separated by two quantum phase transitions. We show that the two quantum critical points are all in the three-dimensional O(3) universality class. The properties of the two gapped phases, including the finite-size behavior of the string orders in the Haldane phase, are studied. We show that the surface formed by the ladder ends is gapless, while the surface exposed along the ladder is gapful in the Haldane phase. Conversely, in the gapped rung singlet phase, the former surface is gapped, and the latter is gapless. We demonstrate that, although the mechanisms of the two gapless modes are different, nonordinary surface critical behaviors are realized at both critical points on the gapless surfaces exposed by simply cutting bonds without fine-tuning the surface coupling required to reach a multicritical point in classical models. We also show that, on the gapped surfaces, the surface critical behaviors are in the ordinary class.

We present a detailed study of the magnetic properties of weakly ferromagnetic/quantum critical ${\mathrm{Nb}}_{1-y}{\mathrm{Fe}}_{2+y}$ using muon spin rotation and relaxation ($\mu \mathrm{SR}$). By means of an angular dependent study of the muon spin rotation signal in applied magnetic fields on a single crystal in the paramagnetic state we establish the muon stopping site in the crystallographic lattice of ${\mathrm{NbFe}}_2$. With this knowledge we develop models to describe the muon spin rotation and relaxation signals in the weakly ferromagnetic, spin density wave, and quantum critical phases of ${\mathrm{Nb}}_{1-y}{\mathrm{Fe}}_{2+y}$ and fit the corresponding experimental data. In particular, we quantify the $\mu \mathrm{SR}$ response for quantum critical behavior in ${\mathrm{Nb}}_{1.0117}{\mathrm{Fe}}_{1.9883}$ and extract the influence of residual weak structural disorder. From our analysis, ${\mathrm{Nb}}_{1-y}{\mathrm{Fe}}_{2+y}$ emerges to be uniquely suited to study quantum criticality close to weak itinerant ferromagnetic order.

Starting from an effective two-dimensional two-band model for infinite-layered nickelates, consisting of bands obtained from $d$- and $s$-like orbitals, we investigate to which extent it can be mapped onto a single-band Hubbard model. We identify screening of the more itinerant $s$-like band as an important driver. In the absence of screening one strongly correlated band gives an antiferromagnetic ground state. For weak screening, the strong correlations push electrons out of the $s$ band so that the undoped nickelate remains a Mott insulator with half-filled $d$ orbitals. This regime markedly differs from the observations in high-$T_c$ cuprates and pairing with $s$-wave symmetry would rather be expected in the superconducting state. In contrast, for strong screening, the $s$ and $d_{x^2-y^2}$ bands are both partly filled and couple only weakly, so that one approximately finds a self-doped $d$ band as well as tendencies toward $d$-wave pairing. Particularly in the regime of strong screening mapping to a one-band model gives interesting spectral weight transfers when a second $s$ band is also partly filled. We thus find that both one-band physics and a Kondo-lattice-like regime emerge from the same two-orbital model, depending on the strength of electronic correlations and the size of the $s$-band pocket.