We propose an integrable spin-1 chain with a magnetic impurity whose spin is $1/2$. The integrability of the model is based on an operator solution of the associated reflection equation. Due to the existence of the impurity, the SU(3) symmetry of the bulk is broken. By using the nested algebraic Bethe ansatz, we obtain the exact solution of the system. The eigenvalues, eigenstates, and Bethe ansatz equations are given explicitly. The method provided in this paper can be generalized to other high-rank quantum integrable systems with magnetic impurities where the spins of the bulk and of impurities are different.

This paper presents a mathematical and numerical analysis of the flat-band wave functions occurring in the chiral model of twisted bilayer graphene at the “magic” twist angles. We show that the chiral model possesses an exact intravalley inversion symmetry. Writing the flat-band wave function as a product of a lowest Landau level quantum Hall state and a spinor, we show that the components of the spinor are antiquantum Hall wave functions related by the inversion symmetry operation introduced here. We then show numerically that as one moves from the lowest to higher magic angles, the spinor components of the wave function exhibit an increasing number of zeros, resembling the changes in the quantum Hall wave function as the Landau level index is increased. The wave function zeros are characterized by a chirality, with zeros of the same chirality clustering near the center of the moiré unit cell, while opposite chirality zeros are pushed to the boundaries of the unit cell. The enhanced phase winding at higher magic angles suggests an increased circulating current. Physical implications for scanning tunneling spectroscopy, orbital magnetization and interaction effects are discussed.

We study self-gravitating bosonic systems, candidates for dark-matter halos, by carrying out a suite of direct numerical simulations designed to investigate the formation of finite-temperature, compact objects in the three-dimensional (3D) Fourier-truncated Gross-Pitaevskii-Poisson equation (GPPE). This truncation allows us to explore the collapse and fluctuations of compact objects, which form at both zero temperature and finite temperature. We show that the statistically steady state of the GPPE, in the large-time limit and for the system sizes we study, can also be obtained efficiently by tuning the temperature in an auxiliary stochastic Ginzburg-Landau-Poisson equation. We show that, over a wide range of model parameters, this system undergoes a thermally driven first-order transition from a collapsed, compact, Bose-Einstein condensate to a tenuous Bose gas (that is not gravitationally condensed). By a suitable choice of initial conditions in the GPPE, we also obtain a binary condensate that comprises a pair of collapsed objects rotating around their center of mass.

Three-dimensional, commensurate long-range magnetic order in ${\mathrm{La}}_2{\mathrm{CuO}}_4$ quickly evolves to quasi-two-dimensional, incommensurate correlations upon doping with mobile holes, and superconductivity follows for $x$ as small as 0.05 in the ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x/{\mathrm{Ba}}_x{\mathrm{CuO}}_4$ family of superconductors. The onset of superconductivity in these systems is known to be coincident with a remarkable rotation of the incommensurate spin order from “diagonal stripes” below $x$ = 0.05 to “parallel stripes” above. However, little is known about the spin correlations at optimal and high doping levels, around and beyond the proposed quantum critical point for the pseudogap phase, $p^{*}$. Here, we present elastic and inelastic neutron scattering measurements on single crystals of ${\mathrm{La}}_{1.6-x}{\mathrm{Nd}}_{0.4}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ with $x$ = 0.125, 0.19, 0.24, and 0.26 and show that two-dimensional, quasistatic, parallel spin stripes have an onset at temperatures such that the parallel spin stripe phase extends beyond $p^{*}$ and envelops the entirety of superconducting ground states in this system. We also show that the elastic order parameter for parallel spin stripes at optimum doping, $x$ = 0.19, displays an inflection point at superconducting $T_c$, while the low-energy dynamic spectral weight of parallel stripe fluctuations grows with decreasing temperature and saturates below $T_c$.

An efficient representation of a quantum circuit is of great importance in achieving a quantum advantage on current noisy intermediate scale quantum (NISQ) devices and the classical simulation of quantum many-body systems. The quantum circuits are playing the key ingredient in the performance of variational quantum algorithms and quantum dynamics in problems of physics and chemistry. In this paper, we study the role of the network structure of a quantum circuit in its performance. We discuss the variational optimization of quantum circuit (a unitary tensor-network circuit) with different network structures. The ansatz is performed based on a generalization of well-developed multiscale entanglement renormalization algorithm and also the conjugate-gradient method with an effective line search. We present the benchmarking calculations for different network structures by studying the Heisenberg model in a strongly disordered magnetic field and a tensor-network $QR$ decomposition. Our work can contribute to achieve the most out of NISQ hardware and to classically develop isometric tensor network states.

Disorder is intrinsic to weakly bound ionic systems and gives rise to specific electronic processes. In recently developed perovskite ionic crystals, this dynamic lattice disorder is inferred to give rise to properties of interest, such as defect tolerance. Here, the elementary excitation of interest is the polaron, a localized lattice distortion. We employ state-resolved pump/probe spectroscopy to monitor electron and lattice dynamics in bulk $\mathrm{CsPb}{\mathrm{Br}}_3$ perovskite crystals. The data report surprising line-shape dynamics. Rather than causing redshifting of the band edge exciton, polaron formation gives rise to confinement induced dynamical processes leading to a blueshift in the band edge bleach feature. In these ionic nanocrystals, the formation of quantum confined excitons arises from the polaronic potential, as opposed to physical confinement in conventional covalent quantum dots, resulting in an excitation of a quantum confined exciton polaron. This state may represent an alternative quasiparticle.

A molecular Mott insulator $\kappa \text{−}{\left(\mathrm{ET}\right)}_2\mathrm{B}{\left(\mathrm{CN}\right)}_4$ [ET = bis(ethylenedithio)tetrathiafulvalene] with a distorted triangular lattice exhibits a quantum disordered state with gapped spin excitation in the ground state. ${}^{13}\mathrm{C}$ nuclear magnetic resonance, magnetization, and magnetic torque measurements reveal that magnetic field suppresses valence bond order and induces long-range magnetic order above a critical field $\sim 8$ T. The nuclear spin-lattice relaxation rate $1/T_1$ shows persistent evolution of antiferromagnetic correlation above the transition temperature, highlighting a quantum spin liquid state with fractional excitations. The field-induced transition as observed in the spin-Peierls phase suggests that the valence bond order transition is driven through renormalized one-dimensionality and spin-lattice coupling.

We report spin-polarized tunneling density of states measurements of the proximity modulated superconductor-insulator transition in ultrathin Be-Al bilayers. The bilayer samples consisted of a Be film of varying thickness, $d_{\mathrm{Be}}=0.8–4.5\mathrm{nm}$, on which a 1 nm thick capping layer of Al was deposited. Detailed measurements of the Zeeman splitting of the BCS coherence peaks in samples with sheet resistances $R\sim h/4e^2$ revealed a superlinear Zeeman shift near the critical field. Our data suggests that critically disordered samples have a broad distribution of gap energies and that only the higher portion of the distribution survives as the Zeeman critical field is approached. This produces a counterintuitive field dependence in which the gap apparently increases with increasing parallel field.

Given the parallelism between the physical properties of Ce- and Yb-based magnets and heavy fermions due to the electron-hole symmetry, it has been rather odd that the transition temperature of the Yb-based compounds is normally very small, as low as $\sim 1\mathrm{K}$ or even lower, whereas Ce counterparts may often have the transition temperature well exceeding 10 K. Here, we report our experimental discovery of the transition temperature reaching 20 K in a Yb-based compound at ambient pressure. The Mn substitution at the Al site in an intermediate valence state of $\alpha \text{−}{\mathrm{YbAlB}}_4$ not only induces antiferromagnetic transition at a record high temperature of 20 K but also transforms the heavy-fermion liquid state in $\alpha \text{−}{\mathrm{YbAlB}}_4$ into a highly resistive metallic state proximate to a Kondo insulator.

$\mathrm{SU}\left(N\right)$ Mott insulators have been proposed and/or realized in solid-state materials and with ultracold atoms on optical lattices. We study the two-dimensional $\mathrm{SU}\left(N\right)$ antiferromagnets on the triangular lattice. Starting from an $\mathrm{SU}\left(N\right)$ Heisenberg model with the fundamental representation on each site in the large-$N$ limit, we perform a self-consistent calculation and find a variety of ground states including the valence cluster states, stripe ordered states with a doubled unit cell, and topological chiral spin liquids. The system favors a cluster or ordered ground state when the number of flavors $N$ is less than 6. It is shown that increasing the number of flavors enhances quantum fluctuations and eventually transfers the clusterized ground states into topological chiral spin liquids. This chiral spin liquid ground state has an equivalent for the square lattice $\mathrm{SU}\left(N\right)$ magnets. We further identify the corresponding lowest competing states that represent another distinct type of chiral spin liquid state. We conclude with a discussion of the relevant systems and the experimental probes.

We investigate topological signatures in the short-time nonequilibrium dynamics of symmetry protected topological (SPT) systems starting from initial states which break a protecting symmetry. Naively one might expect that topology loses meaning when a protecting symmetry is broken. Defying this intuition, we illustrate, in an interacting Su-Schrieffer-Heeger (SSH) model, how this combination of symmetry breaking and quench dynamics can give rise to both single-particle and many-body signatures of topology. From the dynamics of the symmetry broken state, we find that we are able to dynamically probe the equilibrium topological phase diagram of a symmetry respecting projection of the post-quench Hamiltonian. In the ensemble dynamics we demonstrate how spontaneous symmetry breaking (SSB) of a protecting symmetry can result in a quantized many-body topological “invariant” which is not pinned under unitary time evolution. We dub this “dynamical many-body topology” (DMBT). We show numerically that both the pure state and ensemble signatures are remarkably robust, and argue that these nonequilibrium signatures should be quite generic in SPT systems, regardless of protecting symmetries or spatial dimension.

Braiding phases among topological excitations are key data for physically characterizing topological orders. In this paper, we provide a field-theoretical approach toward a complete list of mutually compatible braiding phases of topological orders in $(3+1)\mathrm{D}$ spacetime. More concretely, considering a discrete gauge group as input data, topological excitations in this paper are bosonic particles carrying gauge charges and loops carrying gauge fluxes. Among these excitations, there are three classes of root braiding processes: particle-loop braidings (i.e., the familiar Aharonov-Bohm phase of winding an electric charge around a thin magnetic solenoid), multiloop braidings [Wang and Levin, Phys. Rev. Lett. 113, 080403 (2014)], and particle-loop-loop braidings (i.e., Borromean rings braiding in Chan et al. [Phys. Rev. Lett. 121, 061601 (2018)]). A naive way to exhaust all topological orders is to arbitrarily combine these root braiding processes. Surprisingly, we find that there exist illegitimate combinations in which certain braiding phases cannot coexist, i.e., are mutually incompatible. Thus, the resulting topological orders are illegitimate and must be excluded. It is not obvious to identify these illegitimate combinations. But with the help of the powerful $(3+1)\mathrm{D}$ topological quantum field theories (TQFTs), we find that illegitimate combinations violate gauge invariance. In this way, we are able to obtain all sets of mutually compatible braiding phases and all legitimate topological orders. To illustrate, we work out all details when gauge groups are ${\mathbb{Z}}_{N_1},{\mathbb{Z}}_{N_1}\times {\mathbb{Z}}_{N_2},{\mathbb{Z}}_{N_1}\times {\mathbb{Z}}_{N_2}\times {\mathbb{Z}}_{N_3}$ and ${\mathbb{Z}}_{N_1}\times {\mathbb{Z}}_{N_2}\times {\mathbb{Z}}_{N_3}\times {\mathbb{Z}}_{N_4}$. Finally, we concisely discuss compatible braidings and TQFTs in $(4+1)\mathrm{D}$ spacetime.

Ferromagnetic insulators (FI) can induce a strong exchange field in an adjacent superconductor (S) via the magnetic proximity effect. This manifests as spin splitting of the BCS density of states of the superconductor, an important ingredient for numerous superconducting spintronics applications and the realization of Majorana fermions. A crucial parameter that determines the magnitude of the induced spin splitting in FI/S bilayers is the thickness of the S layer $d$: In very thin samples, the superconductivity is suppressed by the strong magnetism. By contrast, in very thick samples, the spin splitting is absent at distances away from the interface. In this work, we calculate the density of states and critical exchange field of FI/S bilayers of arbitrary thickness. From here, we determine the range of parameters of interest for applications, where the exchange field and superconductivity coexist. We show that for $d>3.0{\xi }_s$, the paramagnetic phase transition is always of the second order, in contrast to the first-order transition in thinner samples at low temperatures. Here ${\xi }_s$ is the superconducting coherence length. Finally, we compare our theory with the tunneling spectroscopy measurements in several $\mathrm{EuS}/\mathrm{Al}/{\mathrm{AlO}}_x/\mathrm{Al}$ samples. If the Al film in contact with the EuS is thinner than a certain critical value, we do not observe superconductivity, whereas, in thicker samples, we find evidence of a first-order phase transition induced by an external field. The complete transition is preceded by a regime in which normal and superconducting regions coexist. We attribute this mixed phase to inhomogeneities of the Al film thickness and the presence of superparamagnetic grains at the EuS/Al interface with different switching fields. The steplike evolution of the tunnel-barrier magnetoresistance supports this assumption. Our results demonstrate on the one hand, the important role of the S layer thickness, which is particularly relevant for the fabrication of high-quality samples suitable for applications. On the other hand, the agreement between theory and experiment demonstrates the accuracy of our theory, which, originally developed for homogeneous situations, is generalized to highly inhomogeneous systems.

Steady-state observables, such as occupation numbers and currents, are crucial experimental signatures in open quantum systems. The time-convolutionless (TCL) master equation, which is both exact and time-local, is an ideal candidate for the perturbative computation of such observables. We develop a diagrammatic approach to evaluate the steady-state TCL generator based on operators rather than superoperators. We obtain the steady-state occupation numbers, extend our formulation to the calculation of currents, and provide a simple physical interpretation of the diagrams. We further benchmark our method on a single noninteracting level coupled to Fermi reservoirs, where we recover the exact expansion to next-to-leading order. The low number of diagrams appearing in our formulation makes the extension to higher orders accessible. Combined, these properties make the steady-state time-convolutionless master equation an effective tool for the calculation of steady-state properties in open quantum systems.

Realizing photonic analogs of the robust, unidirectional edge states of electronic topological insulators would improve our control of light on the nanoscale and revolutionize the performance of photonic devices. Here, we show that new symmetry-protected topological phases can be detected by reformulating energy eigenproblems as Berry curvature eigenproblems. The “Berry bands” span the same eigenspace as the original valence energy bands, but separate into pseudo-spinful and pseudo-spinless subspaces in ${\mathrm{C}}_2\mathcal{T}$-symmetric crystals. We demonstrate the method on the well-known case of Wu and Hu [Phys. Rev. Lett. 114, 223901 (2015)] and a recently discovered fragilely topological crystal, and show that both crystals belong to the same photonic analog of the quantum spin-Hall effect. This work helps unite theory and numerics, and is useful in defining and identifying new symmetry-protected phases in photonics and electronics.

In three dimensions, gapped phases can support “fractonic” quasiparticle excitations, which are either completely immobile or can only move within a low-dimensional submanifold, a peculiar topological phenomenon going beyond the conventional framework of topological quantum field theory. In this work we explore fractonic topological phases using three-dimensional coupled wire constructions, which have proven to be a successful tool to realize and characterize topological phases in two dimensions. We find that both gapped and gapless phases with fractonic excitations can emerge from the models. In the gapped case, we argue that fractonic excitations are mobile along the wire direction, but their mobility in the transverse plane is generally reduced. We show that the excitations in general have infinite-order fusion structure, distinct from previously known gapped fracton models. Like the two-dimensional coupled-wire constructions, many models exhibit gapless (or even chiral) surface states, which can be described by infinite-component Luttinger liquids. However, the universality class of the surface theory strongly depends on the surface orientation, thus revealing a different type of bulk-boundary correspondence unique to fracton phases.

We observe and comprehend the dynamical Coulomb blockade suppression of the electrical conductance across an electronic quantum channel subjected to a temperature difference. A broadly tunable, spin-polarized Ga(Al)As quantum channel is connected on-chip, through a micron-scale metallic node, to a linear $RC$ circuit. The latter is made up of the node's geometrical capacitance $C$ in parallel with an adjustable resistance $R\in \{1/2,1/3,1/4\}\times h/e^2$ formed by 2–4 quantum Hall channels. The system is characterized by three temperatures: Temperatures of the electrons in the large electrodes ($T$) and in the node ($T_{\mathrm{node}}$), and a temperature of the electromagnetic modes of the $RC$ circuit ($T_{\mathrm{env}}$). The temperature in the node is selectively increased by local Joule dissipation, and characterized from current fluctuations. For a quantum channel in the tunnel regime, a close match is found between conductance measurements and tunnel dynamical Coulomb blockade theory. In the opposite near ballistic regime, we develop a theory that accounts for different electronic and electromagnetic bath temperatures, again in very good agreement with experimental data. Beyond these regimes, for an arbitrary quantum channel set in the far out-of-equilibrium situation where the temperature in the node significantly exceeds the one in the large electrodes, the equilibrium (uniform temperature) prediction for the conductance is recovered, albeit at a rescaled temperature $\alpha T_{\mathrm{node}}$.

Typical higher-order topological systems require the fine-tuning of hopping textures and external fields, which considerably hinders their practical realization. Based on a simple picture that corners are “edges” of edges, we determine that in the already-thoroughly-studied monolayer graphene, higher-order topological corner states appear without introducing any additional effects. Unlike quadrupole insulators, owing to degenerate Dirac points in graphene, the emergence of topological corner states depends on the corner angle and edge geometries. We provide a useful expression for the indication of corner states in graphene by the product of Zak phases. We also discuss the methods for experimental detection of the nontrivial higher-order topology in graphene such as the fractional corner anomaly and the disparity of local density of states between trivial and nontrivial corners.

We study ${\mathbb{Z}}_2$ topologically ordered states enriched by translational symmetry by employing a recently developed two-dimensional (2D) bosonization approach that implements an exact ${\mathbb{Z}}_2$ charge-flux attachment in the lattice. Such states can display “weak symmetry breaking” of translations, in which both the Hamiltonian and ground state remain fully translational invariant but the symmetry is “broken” by its anyon quasiparticles, in the sense that its action maps them into a different superselection sector. We demonstrate that this phenomenon occurs when the fermionic spinons form a weak topological superconductor in the form of a 2D stack of one-dimensional Kitaev wires, leading to the amusing property that there is no local operator that can transport the $\pi$-flux quasiparticle across a single Kitaev wire of fermonic spinons without paying an energy gap in spite of the vacuum remaining fully translational invariant. We explain why this phenomenon occurs hand in hand with other previously identified peculiar features such as ground-state degeneracy dependence on the size of the torus and the appearance of dangling boundary Majorana modes in certain ${\mathbb{Z}}_2$ topologically ordered states. Moreover, by extending the ${\mathbb{Z}}_2$ charge-flux attachment to open lattices and cylinders, we construct a plethora of exactly solvable models providing an exact description of their dispersive Majorana gapless boundary modes. We also review the $\mathbb{Z}\times {\left({\mathbb{Z}}_2\right)}^3$ classification of 2D BdG Hamiltonians (class D) enriched by translational symmetry and provide arguments on its robust stability against interactions and self-averaging disorder that preserve translational symmetry.