We generalize the method introduced in Phys. Rev. B 101, 041108 (2020) of extracting information about topological order from the ground state of a strongly correlated two-dimensional system represented by an infinite projected entangled pair state (iPEPS) to non-Abelian topological order. When wrapped on a torus the unique iPEPS becomes a superposition of degenerate and locally indistinguishable ground states. We find numerical symmetries of the iPEPS, represented by infinite matrix product operators (MPO) and their fusion rules. The rules tell us how to combine the symmetries into projectors onto states with well defined anyon flux. A linear structure of the MPO projectors allows for efficient determination for each state its second Renyi topological entanglement entropy on an infinitely long cylinder directly in the limit of infinite cylinder's width. The same projectors are used to compute topological $S$ and $T$ matrices encoding mutual and self-statistics of emergent anyons. The algorithm is illustrated by examples of Fibonacci and Ising non-Abelian string net models.

Naturally occurring hyperbolic plasmonic media is rare, and was only recently observed in the $1{\mathrm{T}}^{\prime }$ phase of ${\mathrm{WTe}}_2$. We elucidate on the physical origin of this strong infrared hyperbolic response, and attribute it to band-nested anisotropic interband transitions. Such a phenomenon does not occur in general anisotropic materials, at least not in their pristine state. However, band-nested anisotropic interband transitions can in principle be induced via proper electronic band nesting. We illustrate this principle and demonstrate a topological elliptic-to-hyperbolic transition in ${\mathrm{MoTe}}_2$ via strain engineering, which is otherwise nonhyperbolic.

We introduce a diagnostic for quantum thermalization based on mixed-state entanglement. Specifically, given a pure state on a tripartite system $ABC$, we study the scaling of entanglement negativity between $A$ and $B$. For representative states of self-thermalizing systems, either eigenstates or states obtained by a long-time evolution of product states, negativity shows a sharp transition from an area-law scaling to a volume-law scaling when the subsystem volume fraction is tuned across a finite critical value. In contrast, for a system with quasiparticles, it exhibits a volume-law scaling irrespective of the subsystem fraction. For many-body localized systems, the same quantity shows an area-law scaling for eigenstates, and volume-law scaling for long-time-evolved product states, irrespective of the subsystem fraction. We provide a combination of numerical observations and analytical arguments in support of our conjecture. Along the way, we prove and utilize a “continuity bound” for negativity: we bound the difference in negativity for two density matrices in terms of the Hilbert-Schmidt norm of their difference.

We report on a comprehensive investigation of the effects of strain and film thickness on the structural and magnetic properties of epitaxial thin films of the prototypal $J_{\mathrm{eff}}=1/2$ compound ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ by advanced x-ray scattering. We find that the ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ thin films can be grown fully strained up to a thickness of 108 nm. By using x-ray resonant scattering, we show that the out-of-plane magnetic correlation length is strongly dependent on the thin film thickness, but independent of the strain state of the thin films. This can be used as a finely tuned dial to adjust the out-of-plane magnetic correlation length and transform the magnetic anisotropy from two-dimensional to three-dimensional behavior by incrementing film thickness. These results provide a clearer picture for the systematic control of the magnetic degrees of freedom in epitaxial thin films of ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ and bring to light the potential for a rich playground to explore the physics of $5d$ transition-metal compounds.

${\mathrm{Co}}_4{\mathrm{Ta}}_2{\mathrm{O}}_9$ exhibits a three-dimensional magnetic lattice based on the buckled honeycomb motif. It shows unusual magnetoelectric effects, including the sign change and nonlinearity. These effects cannot be understood without the detailed knowledge of the magnetic structure. Herein, we report neutron diffraction and direction-dependent magnetic susceptibility measurements on ${\mathrm{Co}}_4{\mathrm{Ta}}_2{\mathrm{O}}_9$ single crystals. Below 20.3 K, we find a long-range antiferromagnetic order in the alternating buckled and flat honeycomb layers of ${\mathrm{Co}}^{2+}$ ions stacked along the $\mathit{c}$ axis. Within experimental accuracy, the magnetic moments lie in the $\mathit{ab}$ plane. They form a canted antiferromagnetic structure with a tilt angle of $\sim {14}^{\circ }$ at 15 K in the buckled layers, while the magnetic moments in each flat layer are collinear. This is directly evidenced by a finite (0, 0, 3) magnetic Bragg peak intensity, which would be absent in the collinear magnetic order. The magnetic space group is $C{2}^{\prime }/c$. It is different from the previously reported $C2/c^{\prime }$ group, also found in the isostructural ${\mathrm{Co}}_4{\mathrm{Nb}}_2{\mathrm{O}}_9$. The revised magnetic structure successfully explains the major features of the magnetoelectric tensor of ${\mathrm{Co}}_4{\mathrm{Ta}}_2{\mathrm{O}}_9$ within the framework of the spin-flop model.

Phonons are fundamentally important for many materials properties, including thermal and electronic transport, superconductivity, and structural stability. Here, we describe a method to compute phonons in correlated materials using state-of-the-art density functional theory $+$ dynamical mean-field theory ($\text{DFT}+\text{DMFT}$) calculations. Our approach combines a robust $\text{DFT}+\text{DMFT}$ implementation to calculate forces with the direct method for lattice dynamics using nondiagonal supercells. The use of nondiagonal instead of diagonal supercells drastically reduces the computational expense associated with the $\text{DFT}+\text{DMFT}$ calculations. We benchmark the method for typical correlated materials (Fe, NiO, MnO, $\mathrm{Sr}{\mathrm{VO}}_3$), testing for $\mathbf{q}$-point grid convergence and different computational parameters of the $\text{DFT}+\text{DMFT}$ calculations. The efficiency of the nondiagonal supercell method allows us to access $\mathbf{q}$-point grids of up to $6\times 6\times 6$. In addition, we discover that, for the small displacements that atoms are subject to in the lattice dynamics calculation, fixing the self-energy to that of the equilibrium configuration is in many cases an excellent approximation that further reduces the cost of the $\text{DFT}+\text{DMFT}$ calculations. This fixed self-energy approximation is expected to hold for materials that are not close to a phase transition. Overall, our work provides an efficient and general method for the calculation of phonons using $\text{DFT}+\text{DMFT}$, opening many possibilities for the study of lattice dynamics and associated phenomena in correlated materials.

The tetragonal compound ${\mathrm{Mn}}_{1.4}\mathrm{PtSn}$ with $D_{2d}$ symmetry recently attracted attention as the first known material that hosts magnetic antiskyrmions, which differ from the skyrmions known so far by their internal structure. The latter have been found in a number of magnets with the chiral crystal structure. In previous works, the existence of antiskyrmions in ${\mathrm{Mn}}_{1.4}\mathrm{PtSn}$ was unambiguously demonstrated in real space by means of Lorentz transmission electron microscopy on thin-plate samples ($\sim 100$ nm thick). In the present study, we used small-angle neutron scattering and magnetic force microscopy to perform reciprocal- and real-space imaging of the magnetic texture of bulk ${\mathrm{Mn}}_{\text{1.4}}\mathrm{PtSn}$ single crystals at different temperatures and in applied magnetic field. We found that the magnetic texture in the bulk differs significantly from that of thin-plate samples. Instead of spin helices or an antiskyrmion lattice, we observe an anisotropic fractal magnetic pattern of closure domains in zero field above the spin-reorientation transition temperature, which transforms into a set of bubble domains in high field. Below the spin-reorientation transition temperature the strong in-plane anisotropy as well as the fractal self-affinity in zero field is gradually lost, while the formation of bubble domains in high field remains robust. The results of our study highlight the importance of dipole-dipole interactions in thin-plate samples for the stabilization of antiskyrmions and identify criteria which should guide the search for potential (anti)skyrmion host materials. Moreover, they provide consistent interpretations of the previously reported magnetotransport anomalies of the bulk crystals.

The weak-coupling renormalization group method is an asymptotically exact method to find superconducting instabilities of a lattice model of correlated electrons. Here we extend it to spin-orbit coupled lattice systems and study the emerging superconducting phases of the Rashba-Hubbard model. Since Rashba-type spin-orbit coupling breaks inversion and spin symmetry, the arising superconducting phases may be a mixture of spin-singlet and spin-triplet states. We study the two-dimensional square lattice as a paradigm and discuss the symmetry properties of the arising spin-orbit coupled superconducting states including helical spin-triplet superconductivity. We also discuss how to best deal with split energy bands within a method which restricts paired electrons to momenta on the Fermi surface.

Time- and angle-resolved photoemission spectroscopy (TR-ARPES) accesses the electronic structure of solids under optical excitation, and is a powerful technique for studying the coupling between electrons and collective modes. One approach to infer electron-boson coupling is through the relaxation dynamics of optically excited electrons, and the characteristic timescales of energy redistribution. A common description of electron relaxation dynamics is through the effective electronic temperature. Such a description requires that thermodynamic quantities are well-defined, an assumption that is generally violated at early delays. Additionally, precise estimation of the nonthermal window—within which effective temperature models may not be applied—is challenging. We perform TR-ARPES on graphite and show that Boltzmann rate equations can be used to calculate the time-dependent electronic occupation function $f(\epsilon ,t)$, and reproduce experimental features given by nonthermal electron occupation. Using this model, we define a quantitative measure of nonthermal electron occupation and use it to define distinct phases of electron relaxation in the fluence-delay phase space. More generally, this approach can be used to inform the nonthermal-to-thermal crossover in pump-probe experiments.

We present a mapping of various correlated multi-impurity Anderson models to a cluster model coupled to a number of effective conduction bands capturing its essential low-energy physics. The major ingredient is the complex single-particle self-energy matrix of the uncorrelated problem that encodes the influence to the host conduction band onto the dynamics of a set of correlated orbitals in a given geometry. While the real part of the self-energy matrix generates an effective hopping between the cluster orbitals, the imaginary part, or hybridization matrix, determines the coupling to the effective conduction electron bands in the mapped model. The rank of the hybridization matrix determines the number of independent screening channels of the problem, and allows the replacement of the phenomenological exhaustion criterion by a rigorous mathematical statement. This rank provides a distinction between multi-impurity models of the first kind and of the second kind. For the latter, there are insufficient screening channels available, so that a singlet ground state must be driven by the intercluster spin correlations. This classification provides a fundamental answer to the question of why ferromagnetic exchange interactions between local moments are irrelevant for the spin-compensated ground state in dilute multi-impurity models, whereas the formation of large spins competes with the Kondo scale in dense impurity arrays, without evoking a spin density wave. The low-temperature physics of three examples taken from the literature are deduced from the analytic structure of the mapped model, demonstrating the potential power of this approach. Numerical renormalization group calculations are presented for up to five-site clusters. We investigate the appearance of frustration-induced non-Fermi-liquid fixed points in the trimer, and demonstrate the existence of several critical points of Kosterlitz-Thouless type at which ferromagnetic correlations suppress the screening of an additional effective spin-$1/2$ degree of freedom.

Here, we study the phase diagram of the Aubry-André-Harper model in the presence of strong interactions as the strength of the quasiperiodic potential is varied. Previous work has established the existence of a many-body localized phase at a large potential strength; here, we find a rich phase diagram in the delocalized regime characterized by spin transport and unusual correlations. We calculate the nonequilibrium steady states of a boundary-driven strongly interacting Aubry-André-Harper model by employing the time-evolving block decimation algorithm on matrix product density operators. From these steady states, we extract spin transport as a function of system size and quasiperiodic potential strength. These data show spin transport going from superdiffusive to subdiffusive well before the localization transition; comparing to previous results, we also find that the transport transition is distinct from a transition observed in the speed of operator growth in the model. We also investigate the correlation structure of the steady state and find an unusual oscillation pattern for intermediate values of the potential strength. The unusual spin transport and quantum correlation structure suggest multiple dynamical phases between the much-studied thermal and many-body localized phases.

Composite Fermi liquid metals arise at certain special filling fractions in the quantum Hall regime and play an important role as parents of gapped states with quantized Hall response. They have been successfully described by the Halperin-Lee-Read (HLR) theory of a Fermi surface of composite fermions coupled to a $U\left(1\right)$ gauge field with a Chern-Simons term. However, the validity of the HLR description when the microscopic system is restricted to a single Landau level has not been clear. Here for the specific case of bosons at filling $\nu =1$, we build on earlier work from the 1990s to formulate a low-energy description that takes the form of a noncommutative field theory. This theory has a Fermi surface of composite fermions coupled to a $U\left(1\right)$ gauge field with no Chern-Simons term but with the feature that all fields are defined in a noncommutative space-time. An approximate mapping of the long-wavelength, small-amplitude gauge fluctuations yields a commutative effective-field theory which, remarkably, takes the HLR form but with microscopic parameters correctly determined by the interaction strength. Extensions to some other composite Fermi liquids, and to other related states of matter are discussed.

Using quantum Monte Carlo (QMC) calculations, we investigate the insulator-metal transition observed in liquid hydrogen at high pressure. Below the critical temperature of the transition from the molecular to the atomic liquid, the fundamental electronic gap closure occurs abruptly, with a small discontinuity reflecting the weak first-order transition in the thermodynamic equation of state. Above the critical temperature, molecular dissociation sets in while the gap is still open. When the gap closes, the decay of the off-diagonal reduced density matrix shows that the liquid enters a gapless, but localized, phase: there is a crossover between the insulating and the metallic liquids. Compared to different density functional theory (DFT) functionals, our QMC calculations provide larger values for the fundamental gap and the electronic density of states close to the band edges, indicating that optical properties from DFT potentially benefit from error cancellations.

We numerically study the entanglement dynamics of free fermions on a cubic lattice with potential disorder following a quantum quench. We focus, in particular, on the metal-insulator transition at a critical disorder strength and compare the results to the putative many-body localization (MBL) transition in interacting one-dimensional systems. We find that at the transition point the entanglement entropy grows logarithmically with time $t$ while the number entropy grows $\sim lnlnt$. This is exactly the same scaling recently found in the MBL phase of the Heisenberg chain with random magnetic fields, suggesting that the MBL phase might be more akin to an extended critical regime with both localized and delocalized states rather than a fully localized phase. We also show that the experimentally easily accessible number entropy can be used to bound the full entanglement entropy of the Anderson model and that the critical properties at the metal-insulator transition obtained from entanglement measures are consistent with those obtained by other probes.

The non-Hermitian skin effect is a unique feature of non-Hermitian systems, in which an extensive number of boundary modes appear under the open boundary conditions. Here, we discover higher-order counterparts of the non-Hermitian skin effect that exhibit new boundary physics. In two-dimensional systems with the system size $L\times L$, while the conventional (first-order) skin effect accompanies $\mathcal{O}\left(L^2\right)$ skin modes, the second-order skin effect accompanies $\mathcal{O}\left(L\right)$ corner skin modes. This also contrasts with Hermitian second-order topological insulators, in which only $\mathcal{O}\left(1\right)$ corner zero modes appear. Moreover, for the third-order skin effect in three dimensions, $\mathcal{O}\left(L\right)$ corner skin modes appear from all $\mathcal{O}\left(L^3\right)$ modes. We demonstrate that the higher-order skin effect originates from intrinsic non-Hermitian topology protected by spatial symmetry. We also show that it accompanies the modification of the non-Bloch band theory in higher dimensions.

Laser-induced manipulation of magnetism at the nanoscale is a rapidly growing research topic with potential for applications in spintronics. In this work, we address the role of the scattering cross section, thermal effects, and laser fluence on the magnetic, structural, and chemical stability of individual magnetic nanoparticles excited by single femtosecond laser pulses. We find that the energy transfer from the fs laser pulse to the nanoparticles is limited by the Rayleigh scattering cross section, which in combination with the light absorption of the supporting substrate and protective layers determines the increase in the nanoparticle temperature. We investigate individual Co nanoparticles (8 to 20 nm in size) as a prototypical model system, using x-ray photoemission electron microscopy and scanning electron microscopy upon excitation with single femtosecond laser pulses of varying intensity and polarization. In agreement with calculations, we find no deterministic or stochastic reversal of the magnetization in the nanoparticles up to intensities where ultrafast demagnetization or all-optical switching is typically reported in thin films. Instead, at higher fluences, the laser pulse excitation leads to photochemical reactions of the nanoparticles with the protective layer, which results in an irreversible change in the magnetic properties. Based on our findings, we discuss the conditions required for achieving laser-induced switching in isolated nanomagnets.

We investigate the Ising model in one, two, and three dimensions using a cumulant method that allows us to determine the Lee-Yang zeros from the magnetization fluctuations in small lattices. By doing so with increasing system size, we are able to determine the convergence point of the Lee-Yang zeros in the thermodynamic limit and thereby predict the occurrence of a phase transition. The cumulant method is attractive from an experimental point of view since it uses fluctuations of measurable quantities, such as the magnetization in a spin lattice, and it can be applied to a variety of equilibrium and nonequilibrium problems. We show that the Lee-Yang zeros encode important information about the rare fluctuations of the magnetization. Specifically, by using a simple ansatz for the free energy, we express the large-deviation function of the magnetization in terms of Lee-Yang zeros. This result may hold for many systems that exhibit a first-order phase transition.

The recent discovery of superconductivity in Sr-doped ${\mathrm{NdNiO}}_2$ films grown on ${\mathrm{SrTiO}}_3$ started a novel field within unconventional superconductivity. To understand the similarities and differences between nickelate and cuprate layers on the same ${\mathrm{SrTiO}}_3$ substrate, here based on the density functional theory we have systematically investigated the structural, electronic, and magnetic properties of ${\mathrm{NdNiO}}_2$/${\mathrm{SrTiO}}_3$ and ${\mathrm{CaCuO}}_2$/${\mathrm{SrTiO}}_3$ systems. Our results revealed a strong lattice reconstruction in the case of ${\mathrm{NdNiO}}_2$/${\mathrm{SrTiO}}_3$, resulting in a polar film, with the surface and interfacial ${\mathrm{NiO}}_2$ layers presenting opposite displacements. To avoid the “polar catastrophe,” the ${\mathrm{NiO}}_2$ surface to the vacuum reconstructs as well. However, for ${\mathrm{CaCuO}}_2$/${\mathrm{SrTiO}}_3$, the distortions of those same two ${\mathrm{CuO}}_2$ layers were in the same direction. In addition, we found this distortion to be approximately independent of the studied range of film thickness for the nickelate films. Furthermore, we also observed a two-dimensional electron gas at the interface between ${\mathrm{NdNiO}}_2$ and ${\mathrm{SrTiO}}_3$, caused by the polar discontinuity, in agreement with recent literature. For ${\mathrm{NdNiO}}_2$/${\mathrm{SrTiO}}_3$ the two-dimensional electron gas extends over several layers, while for ${\mathrm{CaCuO}}_2$/${\mathrm{SrTiO}}_3$ this electronic rearrangement is very localized at the interface between ${\mathrm{CaCuO}}_2$ and ${\mathrm{SrTiO}}_3$. The electronic reconstruction found at the interface involves a strong occupation of the Ti $3d_{xy}$ state. In both cases, there is a significant electronic charge transfer from the surface Ni or Cu layers to the Ti interface layer. The interfacial Ni and Cu layers are hole and electron doped, respectively. By introducing magnetism and electronic correlation, we observed that the $d_{3z^2-r^2}$ orbital of Ni becomes itinerant while the same orbital for Cu remains doubly occupied, establishing a clear two- vs one-orbital active framework for the description of these systems. Furthermore, we also observed a strong magnetic reconstruction at the ${\mathrm{NdNiO}}_2$ surface to vacuum layer where magnetism is basically suppressed.

Superconductivity is a macroscopic quantum phenomenon that requires electron pairs to delocalize over large distances. A long-standing question is whether superconductivity can exist even if the electrons' kinetic energy is completely quenched, as is the case in a flat band. This is fundamentally a nonperturbative problem, since the interaction energy scale is the only relevant energy scale, and hence it requires going beyond the traditional Bardeen-Cooper-Schrieffer theory of superconductivity, which is perturbative by nature. In this work, we study a two-dimensional model of an isolated narrow band at partial filling with local attractive interactions, using numerically exact quantum Monte Carlo calculations. We focus on the case where the flat bands are topologically nontrivial, and hence the single-particle wave functions that span these bands cannot be completely spatially localized. Our calculations unambiguously demonstrate that the ground state is a superconductor; strikingly, the critical temperature scales nearly linearly with the interaction strength. Above the superconducting transition temperature, we find a broad pseudogap regime that exhibits strong pairing fluctuations and a tendency towards electronic phase separation. Introducing a small nearest-neighbor attraction suppresses superconductivity entirely and drives the system to phase separate. We discuss the possible relevance of superconductivity in this unusual regime to the physics of flat band moiré materials.

We present an infinite density-matrix renormalization group (DMRG) study of an interacting continuum model of twisted bilayer graphene (tBLG) near the magic angle. Because of the long-range Coulomb interaction and the large number of orbital degrees of freedom, tBLG is difficult to study with standard DMRG techniques—even constructing and storing the Hamiltonian already poses a major challenge. To overcome these difficulties, we use a recently developed compression procedure to obtain a matrix product operator representation of the interacting tBLG Hamiltonian which we show is both efficient and accurate even when including the spin, valley, and orbital degrees of freedom. To benchmark our approach, we focus mainly on the spinless, single-valley version of the problem where, at half filling, we find that the ground state is a nematic semimetal. Remarkably, we find that the ground state is essentially a $k$-space Slater determinant, so that Hartree-Fock and DMRG give virtually identical results for this problem. Our results show that the effects of long-range interactions in magic angle graphene can be efficiently simulated with DMRG and open up a new route for numerically studying strong correlation physics in spinful, two-valley tBLG, and other moiré materials in future work.