Understanding the spreading of the operator space entanglement entropy (OSEE) is key in order to explore out-of-equilibrium quantum many-body systems. Here we argue that for integrable models the dynamics of the OSEE is related to the diffusion of the operator front. We derive the logarithmic bound $1/2ln\left(t\right)$ for the OSEE of some simple, i.e., low-rank, diagonal local operators. We numerically check that the bound is saturated in the rule 54 chain, which is representative of interacting integrable systems. Remarkably, the same bound is saturated in the spin-1/2 Heisenberg $XXZ$ chain. Away from the isotropic point and from the free-fermion point, the OSEE grows as $1/2ln\left(t\right)$, irrespective of the chain anisotropy, suggesting universality. Finally, we discuss the effect of integrability breaking. We show that strong finite-time effects are present, which prevent us from probing the asymptotic behavior of the OSEE.

The simple update (SU) and full update (FU) are the two paradigmatic time evolution algorithms for a tensor network known as the infinite projected entangled pair state (iPEPS). They differ by an error measure that is either, respectively, local or takes into account full infinite tensor environment. In this paper we test an intermediate neighborhood tensor update (NTU) accounting for the nearest-neighbor environment. This small environment can be contracted exactly in a parallelizable way. It provides an error measure that is Hermitian and non-negative down to machine precision. In the two-dimensional quantum Ising model, NTU is shown to yield stable unitary time evolution following a sudden quench. It also yields accurate thermal states despite correlation lengths that reach up to 20 lattice sites. The latter simulations were performed with a manifestly Hermitian purification of a thermal state. Both were performed with reduced tensors that do not include physical (and ancilla) indices. This modification naturally leads to two other schemes: a local SVD update and a full tensor update being a variant of FU.

Magnon transfer torque (MTT) is regarded as capable of manipulating spin by magnons or spin waves only without spatial movement of electrons, which is a key to enrich the toolbox for magnonics. Here using a magnon current through an antiferromagnetic NiO spacer, which can be deep into a magnetic insulator ${\mathrm{Y}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$ (YIG), we demonstrated the perpendicular magnetization of the YIG in a YIG/NiO/Pt heterostructure could be switched. When the thickness of the magnon channel NiO was 1.5 nm, the magnon current could still maintain about $84\%$ of the spin current for the YIG/Pt control device, indicating high efficiency of the NiO spacer in transferring magnon torque. Switching the perpendicular magnetization in the YIG/NiO/Pt heterostructures unambiguously verified the effect of magnon transfer torque (MTT), which may advance the development of magnonic memories and logics.

Recent experiments suggest a quantum spin liquid ground state in the material ${\mathrm{PbCuTe}}_2{\mathrm{O}}_6$, where $S=1/2$ moments are coupled by antiferromagnetic Heisenberg interactions into a three-dimensional structure of corner sharing triangles dubbed the hyper-hyperkagome lattice. It exhibits a richer connectivity, and thus likely a stronger geometric frustration, than the relatively well studied hyperkagome lattice. Here, we investigate the possible quantum spin liquids in the $S=1/2$ hyper-hyperkagome magnet using the complex fermion mean field theory. Extending the results of a previous projective symmetry group analysis, we identify only two ${\mathbb{Z}}_2$ spin liquids and a $U\left(1\right)$ spin liquid that are compatible with the hyper-hyperkagome structure. The $U\left(1\right)$ spin liquid has a spinon Fermi surface. For the ${\mathbb{Z}}_2$ spin liquids, one has a small excitation gap, while the other is gapless and proximate to the $U\left(1\right)$ spin liquid. We show that the gapped and gapless spin liquids can in principle be distinguished by heat capacity measurements. Moreover, we calculate the dynamical spin structure factors of all three spin liquids and find that they highly resemble the inelastic neutron scattering spectra of ${\mathrm{PbCuTe}}_2{\mathrm{O}}_6$. Implications of our work to the experiments, as well as its relations to the existing theoretical studies, are discussed.

Chiral superconductors are expected to carry a spontaneous, chiral, and perpetual current along the sample edge. However, despite the availability of several candidate materials, such a current has not been observed in experiments. In this paper, we suggest an alternative probe in the form of impurity-induced chiral currents. We first demonstrate that a single nonmagnetic impurity induces an encircling chiral current. Its direction depends on the chirality of the order parameter and the sign of the impurity potential. Building on this observation, we consider the case of multiple impurities, e.g., realized as adatoms deposited on the surface of a candidate chiral superconductor. We contrast the responses that are obtained in two cases: (a) when the impurities are all identical in sign and (b) when the impurities have mixed positive and negative signs. The former leads to coherent currents within the sample, arising from the fusion of individual current loops. The latter produces loops of random chirality that lead to incoherent local currents. These two scenarios can be distinguished by measuring the induced magnetic field using recent probes such as diamond nitrogen-vacancy (NV) centers. We argue that impurity-induced currents may be easier to observe than edge currents, as they can be tuned by varying impurity strength, concentration, and correlations. We demonstrate these results using a toy model for $p_x\pm i{p}_y$ superconductivity on a square lattice. We develop an improved scheme for Bogoliubov–de Gennes simulations in which both the order parameter and the magnetic field are determined self-consistently.

In this study we examine the superconducting instability of a quasi-one-dimensional lattice in the Hubbard model based on the random-phase approximation (RPA) and the fluctuation exchange (FLEX) approximation. We find that a spin-singlet pair density wave (PDW singlet) with a center-of-mass momentum of $2k_F$ can be stabilized when the one dimensionality becomes prominent toward the perfect nesting of the Fermi surface. The obtained pair is a mixture of even-frequency and odd-frequency singlet ones. The dominant even-frequency component does not have nodal lines on the Fermi surface. This PDW-singlet state is more favorable as compared to RPA when self-energy correction is introduced in the FLEX approximation.

The effect of disorder in high-$T_{\mathrm{c}}$ superconductors is investigated from the viewpoint of photoinduced quasiparticle (QP) dynamics, obtained through time-resolved pump-probe spectroscopy. We perform the measurements on an optimally doped (OPD) ${\mathrm{Bi}}_{2+x}{\mathrm{Sr}}_{2-x}{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ (Bi2212) with an out-of-plane disorder induced by Bi-Sr substitution $\left(x\right)$, which is present in standard Bi2212 but is not usually controlled. Based on the systematic change of the disorder with controlled $x$, we identify the changes in the dynamics of QP relaxation and gap formation in superconducting (SC) and pseudogap (PG) states. The onset temperature $T^{*}$ of the PG response increases with an increase in $x$, which is more significant than the slight decrease in $T_{\mathrm{c}}$. These properties are equivalently reflected in the destruction fluences of the SC and PG states. Bi-Sr substitution also accelerates relaxation times for SC and PG QPs, which can be due to the increased phonon scattering probability caused by the disorder. In contrast, the SC gap recovery observed in the strongly excited condition shows an identical fluence dependence for various $x$, implying that the disorder does not significantly contribute to coherent gap formation.

Coupling among conduction electrons (e.g., Zhang-Rice singlet) are often manifested in the core level spectra of exotic materials such as cuprate superconductors, manganites, etc. These states are believed to play key roles in the ground state properties and appear as low binding energy features. To explore such possibilities in the Fe-based systems, we study the core level spectra of a superconductor $\mathrm{Ca}{\mathrm{Fe}}_{1.9}{\mathrm{Co}}_{0.1}{\mathrm{As}}_2$ (CaCo122) in the $\mathrm{Ca}{\mathrm{Fe}}_2{\mathrm{As}}_2$ (Ca122) family employing high-resolution hard x-ray photoemission spectroscopy. While As core levels show almost no change with doping and cooling, the Ca $2p$ peak of CaCo122 shows reduced surface contribution relative to Ca122 and a gradual shift of the peak position towards lower binding energies with cooling. In addition, we discover the emergence of a feature at the lower binding energy side of the well-screened Fe $2p$ signal in CaCo122. The intensity of this feature grows with cooling and indicates additional channels to screen the core holes. The evolution of this feature in the superconducting composition and its absence in the parent compound suggests relevance of the underlying interactions in the ground state properties of this class of materials. These results reveal another dimension in the studies of Fe-based superconductors and the importance of such states in the unconventional superconductivity in general.

Accurate phase diagram calculation from molecular dynamics requires systematic treatment and convergence of statistical averages. In this work we propose a Gaussian process regression based framework for reconstructing the free-energy functions using data of various origins. Our framework allows for propagating statistical uncertainty from finite molecular dynamics trajectories to the phase diagram and automatically performing convergence with respect to simulation parameters. Furthermore, our approach provides a way for automatic optimal sampling in the simulation parameter space based on a Bayesian optimization approach. We validate our methodology by constructing phase diagrams of two model systems, the Lennard-Jones and soft-core potential, and compare the results with the existing studies and our coexistence simulations. Finally, we construct the phase diagram of lithium at temperatures above 300 K and pressures below 30 GPa from a machine-learning potential trained on ab initio data. Our approach performs well when compared to coexistence simulations and experimental results.

Neural quantum states are a recently introduced class of variational many-body wave functions that are very flexible in approximating diverse quantum states. Optimization of an NQS ansatz requires sampling from the corresponding probability distribution defined by squared wave function amplitude. For this purpose, we propose to use kinetic sampling protocols and demonstrate that in many important cases such methods lead to much smaller autocorrelation times than the Metropolis-Hastings sampling algorithm while still allowing to easily implement lattice symmetries (unlike autoregressive models). We also use uniform manifold approximation and projection algorithm to construct two-dimensional isometric embedding of Markov chains and show that kinetic sampling helps attain a more homogeneous and ergodic coverage of the Hilbert space basis.

Crystallographic point group symmetry (CPGS) such as polar and nonpolar crystal classes have long been known to classify compounds that have spin-orbit-induced spin splitting. While taking a journey through the Brillouin zone (BZ) from one $k$-point to another for a fixed CPGS, it is expected that the wave vector point group symmetry (WPGS) can change, and consequently, a qualitative change in the texture of the spin polarization can occur [the expectation value of spin operator ${\vec{S}}_{n{k}_0}$ in Bloch state $u\left(n,k\right)$ and the wave vector $k_0$]. However, the nature of the spin texture (ST) change is generally unsuspected. In this paper, we determine a full classification of the linear-in-$k$ ST patterns based on the polarity and chirality reflected in the WPGS at $k_0$. The spin-polarization vector ${\vec{S}}_{n{k}_0}$ controlling the ST is bound to be parallel to the rotation axis and perpendicular to the mirror planes, and hence, symmetry operation types in WPGSs impose symmetry restriction to the ST. For instance, the ST is always parallel to the wave vector $k$ in nonpolar chiral WPGSs since they contain only rotational symmetries. Some consequences of the ST classification based on the symmetry operations in the WPGS include the observation of ST patterns that are unexpected according to the symmetry of the crystal. For example, it is usually established that spin-momentum locking effect (spin vector always perpendicular to the wave vector) requires the crystal inversion symmetry breaking by an asymmetric electric potential. However, we find that polar WPGS can have this effect even in compounds without electric dipoles or external electric fields. We use the determined relation between WPGS and ST as a design principle to select compounds with multiple STs near band edges at different $k$ valleys. Based on high-throughput calculations for 1481 compounds, we find 37 previously fabricated materials with different STs near band edges. The ST classification as well as the predicted compounds with multiple STs can be a platform for potential application for spin-valleytronics and the control of the ST by accessing different valleys.

We introduce a classical limit of the dynamics of quantum spin systems based on coherent states of $\mathrm{SU}\left(N\right)$, where $N$ is the dimension of the local Hilbert space. This approach, which generalizes the well-known Landau-Lifshitz dynamics from SU(2) to $\mathrm{SU}\left(N\right)$, provides a better approximation to the exact quantum dynamics for a large class of realistic spin Hamiltonians, including $S\ge 1$ systems with large single-ion anisotropy and weakly coupled multispin units, such as dimers or trimers. We illustrate this idea by comparing the spin structure factors of a single-ion $S=1$ model that are obtained with the SU(2) and SU(3) classical spin dynamics against the exact solution.

We generally expect quantum systems to thermalize and satisfy the eigenstate thermalization hypothesis (ETH), which states that finite-energy-density eigenstates are thermal. However, some systems, such as many-body localized systems and systems with quantum many-body scars, violate ETH and have high-energy athermal eigenstates. In systems with scars, most eigenstates thermalize, but a few atypical scar states do not. Scar states can give rise to a periodic revival when time-evolving particular initial product states, which can be detected experimentally. Recently, a family of spin Hamiltonians was found with magnetically ordered three-colored eigenstates that are quantum many-body scars [Lee et al., Phys. Rev. B 101, 241111(R) (2020)]. These models can be realized in any lattice that can be tiled by triangles, such as the triangular or kagome lattices, and have been shown to have close connections to the physics of quantum spin liquids in the Heisenberg kagome antiferromagnet. In this paper, we introduce a generalized family of $n$-colored Hamiltonians with “spiral colored” eigenstates made from $n$-spin motifs such as polygons or polyhedra. We show how these models can be realized in many different lattice geometries and provide numerical evidence that they can exhibit quantum many-body scars with periodic revivals that can be observed by time-evolving simple product states. The simple structure of these Hamiltonians makes them promising candidates for future experimental studies of quantum many-body scars.

The cerium-based compound $\mathrm{Ce}{\mathrm{Pt}}_6{\mathrm{Al}}_3$, in which Ce atoms form a honeycomb lattice hosting magnetic frustration, has a heavy-fermion ground state. We have observed development of magnetic order in partially Pd-substituted $\mathrm{Ce}{\left({\mathrm{Pt}}_{1-x}{\mathrm{Pd}}_x\right)}_6{\mathrm{Al}}_3$ series up to $x$ = 0.3 by the measurements of magnetic susceptibility, electrical resistivity ρ, and specific heat $C$. In the whole range of $x$, the unit cell volume remains unchanged within 0.2%, and the effective magnetic moment stays at $2.4{\mu }_B/\mathrm{Ce}$. For $x$ = 0.05, both $C/T$ and $\rho \left(T\right)$ jump on cooling at $T_m=1.8\mathrm{K}$. With increasing $x$ to 0.2, $T_m$ increases to 3.8 K, where $C/T$ shows a pronounced λ-type anomaly. Application of magnetic fields suppresses $T_m$, which is indicative of an antiferromagnetic (AFM) ordered state. Thus, a long-range AFM order is induced by the substitution of isovalent Pd for Pt in $\mathrm{Ce}{\mathrm{Pt}}_6{\mathrm{Al}}_3$ without carrier doping and chemical pressure. We attribute the emergence of AFM order in $\mathrm{Ce}{\left({\mathrm{Pt}}_{1-x}{\mathrm{Pd}}_x\right)}_6{\mathrm{Al}}_3$ to the randomness in the spin-orbit interaction in the Pt-Pd sublattice, which weakens both the coherent Kondo effect and magnetic frustration in the honeycomb Kondo lattice.

The discovery by Kane and Mele of a model of spinful electrons characterized by a ${\mathcal{Z}}_2$ topological invariant had a lasting effect on the study of electronic band structures. Given this, it is natural to ask whether similar topology can be found in the bandlike excitations of magnetic insulators, and recently models supporting ${\mathcal{Z}}_2$ topological invariants have been proposed for both magnon [H. Kondo et al., Phys. Rev. B 99, 041110(R) (2019)] and triplet [D. G. Joshi and A. P. Schnyder, Phys. Rev. B 100, 020407(R) (2019)] excitations. In both cases, magnetic excitations form time-reversal (TR) partners, which mimic the Kramers pairs of electrons in the Kane-Mele model but do not enjoy the same type of symmetry protection. In this paper, we revisit this problem in the context of the triplet excitations of a spin model on the bilayer kagome lattice. Here the triplet excitations provide a faithful analog of the Kane-Mele model as long as the Hamiltonian preserves the $\mathrm{TR}\times \mathrm{U}$(1) symmetry. We find that exchange anisotropies, allowed by the point group and typical in realistic models, break the required $\mathrm{TR}\times \mathrm{U}$(1) symmetry and instantly destroy the ${\mathcal{Z}}_2$ band topology. We further consider the effects of TR breaking by an applied magnetic field. In this case, the lifting of spin degeneracy leads to a triplet Chern insulator, which is stable against the breaking of $\mathrm{TR}\times \mathrm{U}$(1) symmetry. Kagome bands realize both a quadratic and a linear band touching, and we provide a thorough characterization of the Berry curvature associated with both cases. We also calculate the triplet-mediated spin Nernst and thermal Hall signals which could be measured in experiments. These results suggest that the ${\mathcal{Z}}_2$ topology of bandlike excitations in magnets may be intrinsically fragile compared to their electronic counterparts.

Recently, there have been contrary claims of Kitaev spin-liquid behavior and ordered behavior in the honeycomb compound ${\mathrm{Ag}}_3\mathrm{Li}{\mathrm{Ir}}_2{\mathrm{O}}_6$ based on various experimental signatures. Our investigations on this system reveal a low-temperature ordered state with persistent dynamics down to the lowest temperatures. Magnetic order is confirmed by clear oscillations in the muon spin relaxation ($\mu \mathrm{SR}$) time spectrum below 9 K until 52 mK. Coincidentally in ${}^7\mathrm{Li}$ nuclear magnetic resonance, a wipeout of the signal is observed below $\sim 10$ K, which again strongly indicates magnetic order in the low-temperature regime. This is supported by our density functional theory calculations which show an appreciable Heisenberg exchange term in the spin Hamiltonian that favors magnetic ordering. The ${}^7\mathrm{Li}$ shift and spin-lattice relaxation rate also show anomalies at $\sim 50$ K. They are likely related to the onset of dynamic magnetic correlations, but their origin is not completely clear. Detailed analysis of our $\mu \mathrm{SR}$ data is consistent with a coexistence of incommensurate Néel and striped environments. A significant and undiminished dynamical relaxation rate ($\sim 5$ MHz) as seen in $\mu \mathrm{SR}$ deep into the ordered phase indicates enhanced quantum fluctuations in the ordered state.

In extended Kitaev models on the honeycomb lattice, off-diagonal interactions (e.g., the $\mathrm{\Gamma },{\mathrm{\Gamma }}^{\prime }$ terms) can give rise to non-Kitaev quantum spin liquids and several magnetically ordered phases. In the present paper, we dope holes to the system and study the resultant $t\text{−}K\text{−}\mathrm{\Gamma }\text{−}{\mathrm{\Gamma }}^{\prime }$ model using mean-field theory. The interplay between the charge and spin degrees of freedom results in a rich phase diagram. Similar to doped cuprates, superconductors, pseudogap phases, Fermi liquid, strange metal and paramagnetic phase are generated. What is different is that, we obtain more than one superconducting phase (including a topological one) and more than one pseudogap phase no matter what the original spin state is. The Chern number of the topological superconductor is either $\nu =\pm 2$ or $\nu =\pm 1$, depending on the ratio $\mathrm{\Gamma }/\left|K\right|$ in the spin channel. We further find that an intermediate in-plane magnetic field can slightly enlarge the size of the topological superconducting phase.

We have investigated thermoelectric properties of the antiferromagnetic semimetal $\mathrm{Fe}{\mathrm{Ge}}_2$. As temperature decreases from 340 K, the Seebeck coefficient takes a maximum around the Néel temperature and then decreases to show a sign change from positive to negative <50 K. When a strong magnetic field is applied perpendicular to the sample plane, the sign change disappears, and the positive Seebeck coefficient is observed in the whole temperature range. This large magneto-Seebeck effect is anisotropic since the Seebeck coefficient is insensitive to in-plane magnetic fields. Based on the Mott formula, we discuss the origins for this anisotropic magneto-Seebeck effect.

We implement a self-consistent Hartree-Fock approximation based on a microscopic model in real space, which allows us to consider the interplay between the Hubbard and the extended Coulomb interaction in twisted bilayer graphene at the magic angle. These two interactions tend to favor different symmetry-breaking patterns, therefore having complementary roles in the regimes where one or the other dominates. We show that, for sufficiently large values of the on-site Hubbard repulsion, magic angle graphene has an antiferromagnetic ground state at the charge neutrality point, while at half filling of the lowest valence band the state becomes fully spin-polarized. In general, a suitable screening of the extended Coulomb interaction is required to observe the magnetic state in either case, as otherwise the instabilities take place in the charge sector, preferentially in the form of time-reversal, chiral, or valley symmetry breaking.