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arXiv:1806.09674 · Physical review. B./Physical review. B

Suppression of transport in nondisordered quantum spin chains due to confined excitations

Paolo P. Mazza, Gabriele Perfetto, Alessio Lerose, Mario Collura, Andrea Gambassi

Published May 21, 2019• 80 citations
arXivHTMLPDF

Abstract

The laws of thermodynamics require any initial macroscopic inhomogeneity in extended many-body systems to be smoothed out by the time evolution through the activation of transport processes. In generic quantum systems, transport is expected to be governed by a diffusion law, whereas a sufficiently strong quenched disorder can suppress it completely due to many-body localization of quantum excitations. Here, we show that the confinement of quasiparticles can also suppress transport even if the dynamics are generated by nondisordered Hamiltonians. We demonstrate this in the quantum Ising chain with transverse and longitudinal magnetic fields, prepared in a paradigmatic state with a domain wall and thus with a spatially varying energy density. We perform extensive numerical simulations of the dynamics which turn out to be in excellent agreement with an effective analytical description valid within both weak and strong confinement regimes. Our results show that the energy flow from ``hot'' to ``cold'' regions of the chain is suppressed for all accessible times. We argue that this phenomenon is general, as it relies solely on the emergence of confinement of excitations.

DOI
10.1103/physrevb.99.180302

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The laws of thermodynamics require any initial macroscopic inhomogeneity in extended many-body systems to be smoothed out by the time evolution through the activation of transport processes. In generic quantum systems, transport is expected to be governed by a diffusion law, whereas a sufficiently strong quenched disorder can suppress it completely due to many-body localization of quantum excitations. Here, we show that the confinement of quasiparticles can also suppress transport even if the dynamics are generated by nondisordered Hamiltonians. We demonstrate this in the quantum Ising chain with transverse and longitudinal magnetic fields, prepared in a paradigmatic state with a domain wall and thus with a spatially varying energy density. We perform extensive numerical simulations of the dynamics which turn out to be in excellent agreement with an effective analytical description valid within both weak and strong confinement regimes. Our results show that the energy flow from hot'' to cold'' regions of the chain is suppressed for all accessible times. We argue that this phenomenon is general, as it relies solely on the emergence of confinement of excitations.
We show that long-range ferromagnetic interactions in quantum spin chains can induce spatial quasilocalization of topological magnetic defects, i.e., domain walls, even in the absence of quenched disorder. Utilizing matrix-product-states numerical techniques, we study the nonequilibrium evolution of initial states with one or more domain walls under the effect of a transverse field in variable-range quantum Ising chains. Upon increasing the range of these interactions, we demonstrate the occurrence of a sharp transition characterized by the suppression of spatial diffusion of the excitations during the accessible time scale: the excess energy density remains localized around the initial position of the domain walls. This quasilocalization is accurately reproduced by an effective semiclassical model, which elucidates the crucial role that long-range interactions play in this phenomenon. The predictions of this Rapid Communication can be tested in current experiments with trapped ions.
Abstract The phenomenon of many-body localization in disordered quantum many-body systems occurs when all transport is suppressed despite the fact that the excitations of the system interact. In this work we report on the numerical simulation of autonomous quantum dynamics for disordered Heisenberg chains when the system is prepared with an initial inhomogeneity in the energy density profile. Using exact diagonalisation and a dynamical code based on Krylov subspaces we are able to simulate dynamics for up to L = 26 spins. We find, surprisingly, the breakdown of energy diffusion even before the many-body localization transition whilst the system is still in the ergodic phase. Moreover, in the ergodic phase we also find a large region in parameter space where the energy dynamics remains diffusive but where spin transport has been previously evidenced to occur only subdiffusively: this is found to be true for initial states composed of infinitely many hydrodynamic modes (square-wave energy profile) or just the single longest mode (sinusoidal profile). This suggestive finding points towards a peculiar ergodic phase where particles are transported slower than energy, reminiscent of the situation in amorphous solids and of the gapped phase of the anisotropic Heisenberg model.
The study of collective behaviour in many-body systems often explores fundamentally new ideas absent from the mere constituents of such a system. A paradigmatic model for these studies is the spin-1/2 XXZ chain and its fermionic equivalent. This thesis can be broadly divided into the study of two fundamental aspects of this model. Firstly, we discuss localisation phenomena in one dimensional lattices as often experimentally realised in cold atom systems. Secondly, we investigate how disorder and symmetry influence heat transport in spin chains. More specifically, in the first part we consider a system of non-interacting fermions in one dimension subject to a single-particle potential consisting of a strong optical lattice, a harmonic trap, and uncorrelated on-site disorder. We investigate a global inhomogeneous quantum quench and present numerical and analytical results for static and dynamical properties. We show that the approach to the non-thermal equilibrium state is extremely slow and that it implies a sensitivity to disorder parametrically stronger than that expected from Anderson localisation. We also consider the above system in a strong non-uniform electric field. In the non-interacting case, due to Wannier-Stark localisation, the single-particle wave functions are exponentially localised without quenched disorder. We show that this system remains localised in the presence of nearest-neighbour interactions and exhibits physics analogous to models of conventional many-body localisation. The second part explores the hydrodynamics of the disordered XYZ spin chain. Using time-evolving block decimation on open chains of up to 400 spins attached to thermal baths, we probe the energy transport of this system. Our principal findings are as follows. For weak disorder there is a stable diffusive region that persists up to a critical disorder strength that depends on the XY anisotropy. Then, for disorder strengths above this critical value energy transport becomes increasingly subdiffusive.
We investigate entanglement dynamics in bipartite systems governed by inhomogeneous Hamiltonians of the form H=HL+HRH = H_L + H_RH=HL​+HR​, where HL/RH_{L/R}HL/R​ acts only on the left or right region and is homogeneous within each region. Focusing on the XX chain and the transverse-field Ising chain, we derive analytical formulas for the entanglement entropy between the two regions in the hydrodynamic limit of long times. In this regime, fermions incident on the interface undergo scattering, generating entanglement between reflected and transmitted modes. The resulting quasiparticle picture is controlled by the transmission coefficient, which we obtain analytically by solving the stationary lattice Schrödinger equation. Due to the bounded dispersion, strong inhomogeneity suppresses both transport and entanglement growth. We benchmark our analytical predictions against numerical simulations in paradigmatic setups. Finally, we extend the analysis to the interacting XXZ chain using tDMRG. The numerical data show qualitative agreement with the quadratic case: entanglement growth remains suppressed in the strongly inhomogeneous limit. Notably, however, entanglement continues to increase even when transport is suppressed, at least at intermediate times.
The confinement of elementary excitations induces distinctive features in the non-equilibrium quench dynamics. One of the most remarkable is the suppression of entanglement entropy, which in several instances turns out to oscillate rather than grow indefinitely. While the qualitative physical origin of this behavior is clear, till now no quantitative understanding away from the field theory limit was available. Here we investigate this problem in the weak quench limit, when mesons are excited at rest, hindering entropy growth and exhibiting persistent oscillations. We provide analytical predictions of the entire entanglement dynamics based on a Gaussian approximation of the many-body state, which captures numerical data with great accuracy and is further simplified to a semiclassical quasiparticle picture in the regime of weak confinement. Our methods are valid in general and we apply explicitly to two prototypical models: the Ising chain in a tilted field and the experimentally relevant long-range Ising model.
Abstract Integrable systems possess stable families of quasiparticles, which are composite objects (bound states) of elementary excitations. Motivated by recent quantum computer experiments, we investigate bound-state transport in the spin- 1 / 2 anisotropic Heisenberg chain (XXZ chain). Specifically, we consider the sudden vacuum expansion of a finite region A prepared in a non-equilibrium state. In the hydrodynamic regime, if interactions are strong enough, bound states remain confined in the initial region. Bound-state confinement persists until the density of unbound excitations remains finite in the bulk of A. Since region A is finite, at asymptotically long times bound states are ‘liberated’ after the ‘evaporation’ of the unbound excitations. Fingerprints of confinement are visible in the space-time profiles of local spin-projection operators. To be specific, here we focus on the expansion of the p-Néel states, which are obtained by repetition of a unit cell with p up spins followed by p down spins. Upon increasing p, the bound-state content is enhanced. In the limit p → ∞ one obtains the domain-wall initial state. We show that for p < 4, only bound states with n > p are confined at large chain anisotropy. For p ≳ 4 , bound states with n = p are also confined, consistent with the absence of transport in the limit p → ∞ . The scenario of bound-state confinement leads to a hierarchy of timescales at which bound states of different sizes are liberated, which is also reflected in the dynamics of the von Neumann entropy.