Dynamical Localization in Disordered Quantum Spin Systems

We say that a quantum spin system is dynamically localized if the time-evolution of local observables satisfies a zero-velocity Lieb-Robinson bound. In terms of this definition we have the following main results: First, for general systems with short range interactions, dynamical localization implies exponential decay of ground state correlations, up to an explicit correction. Second, the dynamical localization of random xy spin chains can be reduced to dynamical localization of an effective one-particle Hamiltonian. In particular, the isotropic xy chain in random exterior magnetic field is dynamically localized.     

Quasihole Tunneling in Disordered Fractional Quantum Hall Systems

Fractional quantum Hall systems are often described by model wave functions,which are the ground states of pure systems with short-range interaction.A primary example is the Laughlin wave function,which supports Abelian quasiparticles with fractionalized charge.In the presence of disorder,the wave function of the ground state is expected to deviate from the Laughlin form.We study the disorder-driven colla.pse of the quantum Hall state by analyzing the evolution of the ground state and the single-quasihole state.In particular,we demonstrate that the quasihole tunneling amplitude can signal the fractional quantum Hall phase to insulator transition.     

An Anderson Impurity Interacting with the Helical Edge States in a Quantum Spin Hall Insulator

Using the natural orbitals renormalization group(NORG)method,we investigate the screening of the local spin of an Anderson impurity interacting with the helical edge states in a quantum spin Hall insulator.It is found that there is a local spin formed at the impurity site and the local spin is completel.y screened by electrons in the quantum spin Hall insulator.Meanwhile,the local spin is screened dominantly by a single active natural orbital.We then show that the Kondo screening mechanism becomes transparent and simple in the framework of the natural orbitals formalism.We project the active natural orbital respectively into real space and momentum space to characterize its structure.We conilrm the spin-momentum locking property of the edge states based on the occupancy of a Bloch state on the edge to which the impurity couples.Furthermore,we study the dynamical property of the active natural orbital represented by the local density of states,from which we observe the Kondo resonance peak.     

Equilibrium Chiral Edge Currents of the Landau Spin Sublevels

Journal of Experimental and Theoretical Physics - Equilibrium edge currents emerging due to the variation of occupation of individual Landau spin sublevels near the sample edge are calculated for...     

Quantum Spin Hall Effect in a Triple-Well Quantum Dot System

A scheme for generating a quantum spin Hall effect for an ensemble of electrons trapped in a triple-well quantum dot system is proposed. Light-induced effective spin-dependent gauge potential and gauge filed are both given in a real Gaussian pulses space. In our scheme, the spin Hall effect can be demonstrated by electronic population without spin-orbit coupled interaction in the absence of any magnetic fields.     

Edge and Impurity Effects on Quantization of Hall Currents

We consider the edge Hall conductance and show it is invariant under perturbations located in a strip along the edge (decaying perturbations far from the edge are also allowed). This enables us to prove for the edge conductances a general sum rule relating currents due to the presence of two different media located respectively on the left and on the right half plane. As a particular interesting case we put forward a general quantization formula for the difference of edge Hall conductances in semi-infinite samples with and without a confining wall. It implies in particular that the edge Hall conductance takes its ideal quantized value under a gap condition for the bulk Hamiltonian, or under some localization properties for a random bulk Hamiltonian (provided one first regularizes the conductance; we shall discuss this regularization issue). Our quantization formula also shows that deviations from the ideal value occurs if a semi-infinite distribution of impurity potentials is repulsive enough to produce current-carrying surface states on its boundary.UPR 7061 au CNRSUMR 8088 au CNRS     

Convergence in Energy-Lowering (Disordered) Stochastic Spin Systems

We consider stochastic processes, with finite, in which spin flips (i.e., changes of S ^t _x ) do not raise the energy. We extend earlier results of Nanda–Newman–Stein that each site x has almost surely only finitely many flips that strictly lower the energy and thus that in models without zero-energy flips there is convergence to an absorbing state. In particular, the assumption of finite mean energy density can be eliminated by constructing a percolation-theoretic Lyapunov function density as a substitute for the mean energy density. Our results apply to random energy functions with a translation-invariant distribution and to quite general (not necessarily Markovian) dynamics.     

Topological Knots in Quantum Spin Systems

Knot theory provides a powerful tool for understanding topological matters in biology, chemistry, and physics.Here knot theory is introduced to describe topological phases in a quantum spin system. Exactly solvable models with long-range interactions are investigated, and Majorana modes of the quantum spin system are mapped into different knots and links. The topological properties of ground states of the spin system are visualized and characterized using crossing and linking numbers, which capture the geometric topologies of knots and links. The interactivity of energy bands is highlighted. In gapped phases, eigenstate curves are tangled and braided around each other, forming links. In gapless phases, the tangled eigenstate curves may form knots. Our findings provide an alternative understanding of phases in the quantum spin system, and provide insights into one-dimension topological phases of matter.     

Semi-Classical Dynamics in Quantum Spin Systems

We consider two limiting regimes, the large-spin and the mean-field limit, for the dynamical evolution of quantum spin systems. We prove that, in these limits, the time evolution of a class of quantum spin systems is determined by a corresponding Hamiltonian dynamics of classical spins. This result can be viewed as a Egorov-type theorem. We extend our results to the thermodynamic limit of lattice spin systems and continuum domains of infinite size, and we study the time evolution of coherent spin states in these limiting regimes.     

Entropy Production in Quantum Spin Systems

We consider a quantum spin system consisting of a finite subsystem connected to infinite reservoirs at different temperatures. In this setup we define nonequilibrium steady states and prove that the rate of entropy production in such states is nonnegative. Received: 7 June 2000 / Accepted: 5 November 2000     

Large Deviations for Quantum Spin Systems

We consider high temperature KMS states for quantum spin systems on a lattice. We prove a large deviation principle for the distribution of empirical averages , where the X _i 's are copies of a self-adjoint element X (level one large deviations). From the analyticity of the generating function, we obtain the central limit theorem. We generalize to a level two large deviation principle for the distribution of      

Quantum Spin Systems at Positive Temperature

We develop a novel approach to phase transitions in quantum spin models based on a relation to their classical counterparts. Explicitly, we show that whenever chessboard estimates can be used to prove a phase transition in the classical model, the corresponding quantum model will have a similar phase transition, provided the inverse temperature β and the magnitude of the quantum spins satisfy . From the quantum system we require that it is reflection positive and that it has a meaningful classical limit; the core technical estimate may be described as an extension of the Berezin-Lieb inequalities down to the level of matrix elements. The general theory is applied to prove phase transitions in various quantum spin systems with . The most notable examples are the quantum orbital-compass model on and the quantum 120-degree model on which are shown to exhibit symmetry breaking at low-temperatures despite the infinite degeneracy of their (classical) ground state.     

Topological Distillation by Principal Component Analysis in Disordered Fractional Quantum Hall States

We study the behavior of two-dimensional electron gas in the fractional quantum Hall(FQH) regime in the presence of disorder potential. The principal component analysis is applied to a set of disordered Laughlin ground state model wave function to enable us to distill the model wave function of the pure Laughlin state.With increasing the disorder strength, the ground state wave function is expected to deviate from the Laughlin state and eventually leave the FQH phase. We investigate the phase tr...     

Discovery of Two-Dimensional Quantum Spin Hall Effect in Triangular Transition-Metal Carbides

Though the quantum spin Hall effect(QSHE) in two-dimensional(2 D) crystals has been widely explored, the experimental realization of quantum transport properties is only limited to HgTe/CdTe or InAs/GaSb quantum wells. Here we employ a tight-binding model on the basis of d_(z~2), d_(xy), and d_(x~2-y~2) orbitals to propose QSHE in the triangular lattice, which are driven by a crossing of electronic bands at the Γ point. Remarkably, 2 D oxidized Mxenes W_2 M_2 C_3 are ideal materials with nontrivial gap of 0.12 eV, facilitating room-temperature observations in experiments. We also find that the nontrivially topological properties of these materials are sensitive to the cooperative effect of the electron correlation and spin-orbit coupling. Due to the feasible exfoliation from its 3 D MAX phase, our work paves a new direction towards realizing QSHE with low dissipation.