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

Abstract

The laws of thermodynamics require any initial macroscopic inhomogeneity in extended manybody systems to be smoothed out by the time evolution through the activation of transport processes. In generic, non-integrable 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 quasi-particles can also lead to transport suppression even if the dynamics are generated by homogeneous Hamiltonians. We demonstrate this in the quantum Ising chain with transverse and longitudinal magnetic fields in the paradigmatic case of the evolution of domain-wall states. 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 connected with the presence of atypical states in the many-body energy spectrum which violate the eigenstate thermalization hypothesis, as recently reported in the literature.Introduction-Recent times have witnessed an increasing attention in the non-equilibrium dynamics of isolated quantum many-body systems [1][2][3]. This interest has been prompted by an impressive advance in experimental techniques with cold atoms that made it possible to maintain coherent quantum dynamics for sufficiently long times [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. The simplest protocol to drive a system out of equilibrium is the so-called quantum quench [19][20][21], in which the dynamics of the system are monitored after a sudden change of a parameter of its Hamiltonian.In this context, a fundamental question concerns whether and how the transport of globally conserved physical quantities such as particle and energy densities arises in these non-equilibrium quantum many-body systems [22,23]. The spatial spreading of local inhomogeneities in isolated systems is generically expected to obey a diffusion law, whose microscopic origin is usually traced back to the occurrence of inelastic collisions [24,25].These transport processes can be conveniently studied via inhomogeneous quenches [26,27] in which two subsystems initially prepared in two different equilibrium states, are joined by means of a local interaction. In this framework, transport may be enhanced by the existence of stable quasi-particles traveling ballistically with certain characteristic velocities, as in the case of integrable systems. Indeed, around the junction, a non-equilibrium stationary state may arise, supporting ballistic transport and thus finite currents at long times. These currentcarrying states have been investigated in conformal field theories [28][29][30] and in non-interacting models, where, in addition, exact expressions can be obtained for the nonequilibrium profiles of l...

Fredholm determinants, full counting statistics and Loschmidt echo for domain wall profiles in one-dimensional free fermionic chains

“…When presenting our results in the next section, we compare them to the prior work in detail. We remark that inhomogeneous quenches in one-dimensional systems are being addressed in a wider context of interacting integrable models such as the XXZ chain [42,43] (the result of the latter reference for the Loschmidt echo is consistent with our result in the appropriate limit) and nonintegrable models such as the interacting resonant level model [44][45][46][47], nonintegrable Ising spin chain [48] and various models of the molecular and superconducting junctions [49][50][51][52].…”

Confined Quasiparticle Dynamics in Long-Range Interacting Quantum Spin Chains

“…This movitates us to study thermalization in our long-range model. Previous studies of the short-range Ising model have observed rapid (strong) or slow (weak) thermalization of one-point functions for different initial states [41,42,48,49,[73][74][75][76]. As first shown in Ref.…”

Signatures of rare states and thermalization in a theory with confinement

“…The lattice model (33) has been investigated extensively, with the quench dynamics receiving particular attention. 25,102,[109][110][111][112][113][114] Bañuls et al 109 showed that certain initial states do not appear to thermalize, in spite of the lack of integrability. It is thought that this is linked to the presence of rare states in the spectrum.…”