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arXiv:2004.12738 · Physical review. B./Physical review. B

Long-range interaction in an open boundary-driven Heisenberg spin lattice: A far-from-equilibrium transition to ballistic transport

Manuel Katzer, Willy Knorr, Regina Finsterhölzl, Alexander Carmele

Published Sep 1, 2020• 9 citations
arXivHTMLPDF

Abstract

We study an open Heisenberg XXZ spin chain with long-range Ising-type interaction, which is incoherently driven at its boundaries and, therefore, a far-from-equilibrium steady-state current is induced. Quantum Monte Carlo techniques make a regime accessible where the system size is large enough to examine the transition from a diffusive to a ballistic transport regime. We find that the chain lengths for this transition are increasing with decreasing range of the Ising-type interactions between distant spins, whereas the strength of the incoherent driving does not have a relevant effect on the transport transition. The transition can be explained by the suppression of ferromagnetic domains at the edges of the chain.

DOI
10.1103/physrevb.102.125101

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We study an open Heisenberg XXZ spin chain with long-range Ising-type interaction, which is incoherently driven at its boundaries and, therefore, a far-from-equilibrium steady-state current is induced. Quantum Monte Carlo techniques make a regime accessible where the system size is large enough to examine the transition from a diffusive to a ballistic transport regime. We find that the chain lengths for this transition are increasing with decreasing range of the Ising-type interactions between distant spins, whereas the strength of the incoherent driving does not have a relevant effect on the transport transition. The transition can be explained by the suppression of ferromagnetic domains at the edges of the chain.
We investigate the Heisenberg XXZXXZXXZ chain with long-range interactions in the ZZZ dimension. By applying two magnetic boundary reservoirs, we drive the system out of equilibrium and induce a nonzero steady-state current. The long-range coupled chain shows nearly ballistic transport and linear response for all potential differences of the external reservoirs. In contrast, the common isotropic nearest-neighbor coupling shows negative differential conductivity and a transition from diffusive to subdiffusive transport for a far-from-equilibrium driving. Adding disorder, the change in the transport for nearest-neighbor coupling is therefore highly dependent on the driving. We find for the disordered long-range coupled XXZXXZXXZ chain, any change in the transport behavior is independent of the potential difference and the coupling strengths of the external reservoirs.
In the study of quantum transport, much has been known about dynamics near thermal equilibrium. However, quantum transport far away from equilibrium is much less well understood---the linear response approximation does not hold for physics far out of equilibrium in general. In this work, motivated by recent cold atom experiments on probing quantum many-body dynamics of a one-dimensional XXZ spin chain, where a transition from ballistic to diffusive dynamics has been established by increasing the interaction strengths, we study the strong interaction limit of the one-dimensional spinless fermion model, which is dual to the XXZ spin chain. We develop a highly efficient computation algorithm for simulating the nonequilibrium dynamics of this system exactly, and examine the nonequilibrium dynamics starting from a density modulation quantum state. We find ballistic transport in this strongly correlated setting and show that a plane-wave description emerges at long-time evolution. We also observe a sharp distinction between transport velocities in short and long times as induced by interaction effects and provide a quantitative interpretation for the long-time transport velocity. We expect our results to shed light on the understanding of the dynamics of the XXZ spin chain in the strong interaction regime.
Boundary-driven quantum spin chains are paradigmatic nonequilibrium systems featuring the presence of particle currents. In general, it may not be possible to distinguish an incoherent type of particle transport from a truly quantum coherent one through monitoring the mean current, as both ballistic as well as diffusive regimes occur in either setting. Here, we show that genuine coherent features become manifest in large fluctuations which allow a discrimination between incoherent and coherent quantum transport: in the former case, realizations that are characterized by atypically large boundary activity are associated with larger than typical currents, i.e., an enhanced number of events at the boundaries goes together with a large current. Conversely, in the coherent case the Zeno effect leads to the suppression of current in trajectories with large activity at the boundary. We analyze how these different dynamical regimes are reflected in the structure of rare fluctuations. We show moreover that realizations supporting a large current are generated via weak long-range correlations within the spin chain, typically associated with hyperuniformity. We further observe critical time-coexistence behaviors with intermittent currents in rare fluctuations of the strongly interacting XXZ chain for completely asymmetric drivings.
We study the ballistic-to-diffusive transition induced by the weak breaking of integrability in a boundary-driven XXZ spin chain. Studying the evolution of the spin current density Js{\mathcal{J}}^{s}Js as a function of the system size LLL, we show that, accounting for boundary effects, the transition has a nontrivial universal behavior close to the XX limit. It is controlled by the scattering length ${L}^{*}\ensuremath{\propto}{V}^{\ensuremath{-}2}$, where VVV is the strength of the integrability-breaking term. In the XXZ model, the interplay of interactions controls the emergence of a transient ``quasiballistic'' regime at length scales much shorter than L∗{L}^{*}L∗. This parametrically large regime is characterized by a strong renormalization of the current which forbids a universal scaling, unlike the XX model. Our results are based on matrix product operator numerical simulations and agree with perturbative analytical calculations.
In this work we study the heat transport in an XXZ spin-1/2 Heisenberg chain with homogeneous magnetic field, incoherently driven out of equilibrium by reservoirs at the boundaries. We focus on the effect of bulk dephasing (energy-dissipative) processes in different parameter regimes of the system. The non-equilibrium steady state of the chain is obtained by simulating its evolution under the corresponding Lindblad master equation, using the time evolving block decimation method. In the absence of dephasing, the heat transport is ballistic for weak interactions, while being diffusive in the strongly-interacting regime, as evidenced by the heat-current scaling with the system size. When bulk dephasing takes place in the system, diffusive transport is induced in the weakly-interacting regime, with the heat current monotonically decreasing with the dephasing rate. In contrast, in the strongly-interacting regime, the heat current can be significantly enhanced by dephasing for systems of small size.
We study spin transport in a boundary driven XXZ spin chain. Driving at the chain boundaries is modeled by two additional spin chains prepared in oppositely polarized states. Emergent behavior, both in the transient dynamics and in the long-time quasi-steady state, is demonstrated. Time-dependent matrix-product-state simulations of the system-bath state show ballistic spin transport below the Heisenberg isotropic point. Indications of exponentially vanishing transport are found above the Heisenberg point for low energy initial states while the current decays asymptotically as a power law for high energy states. Precisely at the critical point, non-ballistic transport is observed. Finally, it is found that the sensitivity of the quasi-stationary state on the initial state of the chain is a good witness of the different transport phases.