The bulk helimagnet ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$ represents a unique example in the family of B20 cubic helimagnets exhibiting a tilted spiral and skyrmion phase at low temperatures when the magnetic field is applied along the easy $\langle 001\rangle$ crystallographic direction. Here we present a systematic study of the stability and ordering of these low-temperature magnetic states. We focus our attention on the temperature and field dependencies of the tilted spiral state that we observe persisting up to above $T=35 \mathrm{K}$, i.e., up to higher temperatures than reported so far. We discuss these results in the frame of the phenomenological theory introduced by Dzyaloshinskii in an attempt to reach a quantitative description of the experimental findings. We find that the anisotropy constants, which are the drivers behind the observed behavior, exhibit a pronounced temperature dependence. This explains the differences in the behavior observed at high temperatures (above $T=18 \mathrm{K}$), where the cubic anisotropy is weak, and at low temperatures (below $T=18 \mathrm{K}$), where a strong cubic anisotropy induces an abrupt appearance of the tilted spirals out of the conical state and enhances the stability of skyrmions.

Topologically-ordered phases of matter at nonzero temperature are conjectured to exhibit universal patterns of long-range entanglement, which can be detected using the entanglement negativity, a mixed-state entanglement measure. In this paper, we show that the entanglement negativity in certain topological orders can be understood through the properties of an emergent symmetry-protected topological (SPT) order that is localized on the entanglement bipartition. This connection leads to an understanding of (i) universal contributions to the entanglement negativity, which diagnose finite-temperature topological order and (ii) the behavior of the entanglement negativity across certain phase transitions in which thermal fluctuations eventually destroy long-range entanglement across the bipartition surface. Within this correspondence, the universal patterns of entanglement in the finite-temperature topological order are related to the stability of an emergent SPT order against a symmetry-breaking field. SPT orders protected by higher-form symmetries—which arise, for example, in the description of the entanglement negativity for ${\mathbb{Z}}_2$ topological order in $d=4$ spatial dimensions—remain robust even in the presence of a weak symmetry-breaking perturbation, leading to long-range entanglement at nonzero temperature for certain topological orders.

We present a comprehensive study of vortex structures in $d$-wave superconductors from large-scale renormalized mean-field theory of the square-lattice $t\text{−}{t}^{\prime }\text{−}J$ model, which has been shown to provide a quantitative modeling for high-$T_c$ cuprate superconductors. With an efficient implementation of the kernel polynomial method for solving electronic structures, self-consistent calculations involving up to ${10}^5$ variational parameters are performed to investigate the vortex solutions on lattices of up to ${10}^4$ sites. By taking into account the strong correlation of the model, our calculations shed new light on two puzzling results that have emerged from recent scanning tunneling microscopy experiments. The first concerns the issue of the zero-biased-conductance peak (ZBCP) at the vortex core for a uniform $d$-wave superconducting state. Despite its theoretical prediction, the ZBCP was not observed in most doping range of cuprates except in heavily over-doped samples at low magnetic field. The second issue is the nature of the checkerboard charge-density waves (CDWs) with a period of about eight unit cells in the vortex halo at optimal doping. Although it has been suggested that such bipartite structure arises from low-energy quasiparticle interference, another intriguing scenario posits that the checkerboard CDWs originate from an underlying bidirectional pair-density wave (PDW) ordering with the same period. We present a coherent interpretation of these experimental results based on systematic studies of the doping and magnetic-field effects on vortex solutions with and without a checkerboard structure. Due to the small size of Cooper pairs, the vortex core has a radius of about three unit cells, which results in a strong spatial dependence on pairing fields. This may be an important mechanism for the formation of PDW states inside the vortex core.

Understanding the fundamental mechanisms of optoelectronic excitation and relaxation pathways on the single-molecule level has only recently been started by combining scanning tunneling microscopy (STM) and spectroscopy (STS) with STM-induced luminescence (STML). In this paper, we investigate cationic and anionic fluorescence of individual zinc phthalocyanine (ZnPc) molecules adsorbed on ultrathin NaCl films on Ag(111) by using STML. They depend on the tip-sample bias polarity and appear at threshold voltages that are correlated with the onset energies of particular molecular orbitals, as identified by STS. We also find that the fluorescence is caused by a single-electron tunneling process. Comparing with results from density functional theory calculations, we propose an alternative many-body picture to describe the charging and electroluminescence mechanism. In this paper, we provide aspects toward well-defined voltage selectivity of bipolar electrofluorochromism as well as fundamental insights regarding the role of transiently charged states of emitter molecules within organic light-emitting diode devices.

Helical edge states in topological insulators generate a counterpropagating spin current on the two parallel edges. We here propose antihelical edge states of magnons in patterned antiferromagnetic thin films, which host a copropagating spin current on the two parallel edges, where the two magnon modes with opposite chirality act like the spin. The embedded heavy metal dot array in the thin film induces interfacial Dzyaloshinskii-Moriya interactions (iDMIs), drives the magnon bands into nontrivial topological phases, characterized by spin Chern number. The resulting helical edge modes lead to spin current with the direction dependent on the sign of the iDMI parameter. In a strip geometry, we combine two subsystems with two embedded metal dot arrays, which give opposite iDMI parameters. Antihelical edge states emerge, compensated by the counterpropagating bulk-confined states. Helical and antihelical edge states are verified by the micromagnetic simulations. We consider these results promising and inspiring for further developments of magnon spintronic devices based on antiferromagnets.

Single and double quantum dot (QD) transistors have been used to investigate entropy transitions in the single particle limit. Precisely controlled QD electron states allow a few-particle thermodynamic system to be defined. Charge stability diagrams are calculated to find the Gibbs entropy $S$ vs bias voltage, providing a framework to define single particle entropy diagrams. The calculation method is applied to experimental dopant atom QD transistor characteristics. As multiple states become occupied, $S$ increases in a stepwise manner towards $S=kln\mathrm{\Omega }$, where $\mathrm{\Omega }$ is the total number of microstates, retaining the Boltzmann interpretation of entropy. The $T\text{−}S$ diagram vs gate voltage, where $T$ is temperature, reflects underlying single particle state transitions and enables the definition of heat cycles. These diagrams approximate the behavior of macroscopic phase changes in magnetic, liquid-vapor, and superconducting systems.

We experimentally investigate the stability of a quantum gas with repulsive interactions in an optical one-dimensional lattice subjected to periodic driving. Excitations of the gas in the lowest lattice band are analyzed across the complete stability diagram, from slow to fast driving frequencies and from weak to strong driving strengths. To interpret our results, we expand the established analysis based on parametric instabilities to include modulational instabilities. Extending the concept of modulational instabilities from static to periodically driven systems provides a convenient mapping of the stability in a static system to the cases of slow and fast driving. At intermediate driving frequencies, we observe an interesting competition between modulational and parametric instabilities. We experimentally confirm the existence of both types of instabilities in driven systems and probe their properties. Our results allow us to predict stable and unstable parameter regions for the minimization of heating in future applications of Floquet driving.

We explore the nonequilibrium dynamics of a one-dimensional Fermi-Hubbard system as a sensitive testbed for the capabilities of the time-dependent two-particle reduced density matrix (TD2RDM) theory to accurately describe time-dependent correlated systems. We follow the time evolution of the out-of-equilibrium finite-size Fermi-Hubbard model initialized by a quench over extended periods of time. By comparison with exact calculations for small systems and with matrix product state calculations for larger systems but limited to short times, we demonstrate that the TD2RDM theory can accurately account for the nonequilibrium dynamics in the regime from weak to moderately strong interparticle correlations. We find that the quality of the approximate reconstruction of the three-particle cumulant (or correlation) required for the closure of the equations of motion for the reduced density matrix is key to the accuracy of the numerical TD2RDM results. We identify the size of the dynamically induced three-particle correlations and the amplitude of cross correlations between the two- and three-particle cumulants as critical parameters that control the accuracy of the TD2RDM theory when current state-of-the-art reconstruction functionals are employed.

Two spatially separated magnetic impurities coupled to itinerant electrons give rise to a dynamically generated exchange (RKKY) inter-impurity interaction that competes with the individual Kondo screening of the impurities. It has been recently shown by Yevtushenko and Yudson [Phys. Rev. Lett. 120, 147201 (2018)] that the RKKY interaction and the RKKY vs Kondo competition become nontrivial on helical edges of two-dimensional topological insulators where there is lock-in relation between the electron spin and its direction of motion. Kondo screening always takes over and dominates at large inter-impurity distances and it can also dominate all the way to short distances if the Kondo coupling is sufficiently large and anisotropic. In the present paper, we study the Kondo-RKKY competition in detail on a qualitative and quantitative level. For this we employ the numerically exact numerical renormalization group (NRG) for a broad parameter scan of two Kondo coupled impurities vs magnetic anisotropy, impurity distance, and temperature, and comment on the role of finite bandwidth. We give a pedagogical introduction on the the setup of the two-impurity setting within the NRG in the helical context. Overall we establish a plain crossover from RKKY to Kondo with increasing impurity distance, which permits an intuitive physical picture by simply comparing length scales set by the Kondo screening cloud vs the thermal length scale vs the impurity distance.

We study the relationship between momentum-space spin textures projected onto the occupied bands and Wilson loop winding, proving a map between band topology and spin topology in certain restricted symmetry settings relevant to fragile topology. Our results suggest that, in specific scenarios, the spin gap may act as a smoking gun bulk indicator for fragile topology.

We develop a discrete fermion approach for modeling the strong interaction of an arbitrary system interacting with continuum electronic reservoirs. The approach is based on a pseudofermion decomposition of the continuum bath correlation functions and is only limited by the accuracy of this decomposition. We show that to obtain this decomposition, one can allow for imaginary pseudofermion parameters, and strong damping in individual pseudofermions, without introducing unwanted approximations. For a noninteracting single-resonant level, we benchmark our approach against an analytical solution and an exact hierarchical-equations-of-motion approach. We also show that, for the interacting case, this simple method can capture the strongly correlated low-temperature physics of Kondo resonance, even in the difficult scaling limit, by employing matrix product state techniques.

Recently it has been discovered that in Weyl semimetals the surface state Berry curvature can diverge in certain regions of momentum. This occurs in a continuum description of tilted Weyl cones, which for a slab geometry results in the Berry curvature dipole associated to the surface Fermi arcs growing linearly with slab thickness. Here we investigate analytically incarnations of lattice Weyl semimetals and demonstrate this diverging surface Berry curvature by solving for their surface states and connect these to their continuum descriptions. We show how the shape of the Fermi arc and the Berry curvature hot-line is determined and confirm the $1/k^2$ divergence of the Berry curvature at the end of the Fermi arc as well as the finite-size effects for the Berry curvature and its dipole, using finite-slab calculations and surface Green's function methods. We further establish that apart from affecting the second-order, nonlinear Hall effect, the divergent Berry curvature has a strong impact on other transport phenomena as the Magnus-Hall effect and the nonlinear chiral anomaly.

By combining inelastic neutron scattering and numerical simulations, we study the quasi-one-dimensional Ising-like quantum antiferromagnet ${\mathrm{BaCo}}_2{\mathrm{V}}_2{\mathrm{O}}_8$ in a longitudinal magnetic field applied along the Ising anisotropy, which is also the chain direction. The external field closes the excitation gap due to the magnetic anisotropy, inducing a transition from the Néel ordered state to an incommensurate longitudinal spin density wave phase. If the field is increased further, another transition into a transverse antiferromagnetic phase takes place at 9 T due to the competition between longitudinal and transverse correlations. We numerically and experimentally show that the model of XXZ chains connected by a weak interchain interaction well reproduces this transition. We also calculate the dynamical susceptibility and demonstrate that it agrees quantitatively with inelastic neutron scattering measurements. In contrast to the abrupt change of magnetic ordering, the spectra do not change much at the transition at 9 T, and the spin dynamics can be described as a Tomonaga-Luttinger liquid. We also refine the modeling of ${\mathrm{BaCo}}_2{\mathrm{V}}_2{\mathrm{O}}_8$ by including a four-site periodic term arising from the crystal structure which enables one to account for an anomaly of the magnetic susceptibility appearing at 19.5 T, as well as for the anticrossing observed in the inelastic neutron scattering spectra.

We investigate the anomalous flux state of interacting higher-order topological superconductors (HOTSC) protected by rotation symmetries. By introducing a $\pi$ superconducting flux in 2D HOTSC, we demonstrate the existence of a robust zero mode trapped at the flux center. Remarkably, the rotation symmetry and fermion parity display projective representation inside the $\pi$ flux with $N=2$ supersymmetry algebra. A similar gapless flux pattern also exists in 3D HOTSCs, the flux lines of which carry anomalous helical modes that cannot be realized on purely one-dimensional lattice models. Notably, these exotic phenomena can be manifested in a 2D frustrated quantum magnet whose low energy excitation characterizes emergent Majoranas with HOTSC band structure and the $Z_2$ flux exhibiting supersymmetries.

Dynamical mean-field theory (DMFT) maps the local Green's function of the Hubbard model to that of the Anderson impurity model and thus gives an approximate solution of the Hubbard model from the solution of a simpler quantum impurity model. Accurate solutions to the Anderson impurity model nonetheless become intractable for large systems. Quantum and hybrid quantum-classical algorithms have been proposed to efficiently solve impurity models by preparing and evolving the ground state under the impurity Hamiltonian on a quantum computer that is assumed to have the scalability and accuracy far beyond the current state-of-the-art quantum hardware. As a proof of principle demonstration targeting the Anderson impurity model we, for the first time, close the DMFT loop with current noisy hardware. With a highly optimized fast-forwarding quantum circuit and a noise-resilient spectral analysis we observe both the metallic and Mott-insulating phases. Based on a Cartan decomposition, our algorithm gives a fixed depth, fast-forwarding, quantum circuit that can evolve the initial state over arbitrarily long times without time-discretization errors typical of other product decomposition formulas such as Trotter decomposition. By exploiting the structure of the fast-forwarding circuits we reduce the gate count (to 77 cnots after optimization), simulate the dynamics, and extract frequencies from the Anderson impurity model on noisy quantum hardware. We then demonstrate the Mott transition by mapping both phases of the metal-insulator phase diagram. Near the Mott phase transition, our method maintains accuracy where the Trotter error would otherwise dominate due to the long-time evolution required to resolve quasiparticle resonance frequency extremely close to zero. This work presents the first computation on both sides of the Mott phase transition using noisy digital quantum hardware, made viable by a highly optimized computation in terms of gate depth, simulation error, and runtime on quantum hardware. To inform future computations we analyze the accuracy of our method versus a noisy Trotter evolution in the time domain. Both algebraic circuit decompositions and error mitigation techniques adopted could be applied in an attempt to solve other correlated electronic phenomena beyond DMFT on noisy quantum computers.

We study a variety of Hofstadter ladders in order to probe the interplay between interactions, an applied magnetic field, and crystalline or quasiperiodic geometries. Motion will be induced on charged particles when a magnetic field is present, which can result in exotic distributions of current on a lattice. Typically, the geometry of a ladder lattice is assumed to be homogeneous. In this paper, however, we will study superlattice and quasicrystalline ladders that possess nonuniform bond lengths, in order to study the formation of localized currents. By using density matrix renormalization group (DMRG) to characterize the quantum phases, we confirm the presence of the usual vortex and Meissner distributions of current, in which particles circulate within the bulk and around the edge respectively. Furthermore, it is also possible to observe variations to these patterns; which combine both vortex and Meissner order, and the onset of incompressible domains for specific fillings of the lattice. If the bond lengths of a ladder fluctuate, we find substantial differences to the structure of currents. This is a consequence of an inhomogeneous, effective magnetic flux, resulting in preferential localization of currents throughout the lattice bulk, towards the smaller bond lengths. We then find that incompressible domains can significantly grow in size extent across the parameter space, with currents no longer possessing an extended structure across the longitudinal direction of the ladder.

We propose and experimentally demonstrate the first example of Chern fractal insulators in an acoustic Sierpinski lattice. Through introducing fractality into the well-known Haldane model, we find that the topological phase diagram is significantly squeezed by about 0.5 times, compared with that of the original Haldane model. The energy spectra for different generations of a fractal lattice exhibits a hierarchy of self-similar energy bands in the form of a devil's staircase. With local acoustic measurements, we fabricate the sonic sample based on the theoretical model and experimentally confirm the fractality-induced squeezing and observe the one-way edge states that are protected by a robust mobility gap. Our work demonstrates the fundamental interplay between the fractality and topological Haldane insulator, and may provide new directions for the advanced control of sound waves.