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arXiv:1803.11555 · Physical review. B./Physical review. B

Asymmetry in energy versus spin transport in certain interacting disordered systems

Juan José Mendoza-Arenas, Marko Žnidarič, Vipin Kerala Varma, John Goold, Stephen R. L. Clark, Antonello Scardicchio

Published Mar 22, 2019• 40 citations
arXivHTMLPDF

Abstract

We study energy transport in disordered $XXZ$ spin-1/2 chains driven to nonequilibrium configurations by thermal reservoirs of different temperatures at the boundaries, using large-scale matrix product simulations. In particular we discuss the transition between diffusive and subdiffusive transport in sectors of zero and finite magnetization at high temperature. At large anisotropies we find that diffusive energy transport prevails over a large range of disorder strengths, which is in contrast to spin transport that is subdiffusive in the same regime for weak disorder. However, at finite magnetization both energy and spin currents decay as a function of the system size with the same exponent. We conclude that diffusion of energy is much more pervasive than that of magnetization in these disordered spin-1/2 systems, and occurs across a significant range of the interaction-disorder parameter phase space. We support the existence of this asymmetry, reminiscent of that in the clean limit, by an analytical estimation of diffusion constants for weak disorder.

DOI
10.1103/physrevb.99.094435

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We explore the physics of the disordered XYZ spin chain using two complementary numerical techniques: exact diagonalization (ED) on chains of up to 17 spins, and time-evolving block decimation (TEBD) on chains of up to 400 spins. Our principal findings are as follows. First, we verify that the clean XYZ spin chain shows ballistic energy transport for all parameter values that we investigated. Second, for weak disorder there is a stable diffusive region that persists up to a critical disorder strength that depends on the XY anisotropy. Third, for disorder strengths above this critical value, energy transport becomes increasingly subdiffusive. Fourth, the many-body localization transition moves to significantly higher disorder strengths as the XY anisotropy is increased. We discuss these results, and their relation to our current physical picture of subdiffusion in the approach to many-body localization.
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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.