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arXiv:1706.07744 · Physical review. B./Physical review. B

Boundary-driven Heisenberg chain in the long-range interacting regime: Robustness against far-from-equilibrium effects

Leon Droenner, Alexander Carmele

Published Nov 16, 2017• 11 citations
arXivHTMLPDF

Abstract

We investigate the Heisenberg $XXZ$ chain with long-range interactions in the $Z$ 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 $XXZ$ chain, any change in the transport behavior is independent of the potential difference and the coupling strengths of the external reservoirs.

DOI
10.1103/physrevb.96.184421

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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 spin transport properties of an isotropic quantum Heisenberg spin-chain. Driving the system out of equilibrium via two different reservoirs at the boundaries, the system exhibits negative differential conductivity for strong driving. We describe the system-reservoir interaction with a Lindblad approach. We show that the interplay between Lindblad dynamics and system dynamics influences highly the spin current. For weak driving, equal rates maximize the current while strong driving shows a counter intuitive behavior. Our findings could guide to an understanding of the transport properties which are dependent on the external driving.
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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.
We study transport of local magnetization in spin-1/2 Heisenberg chains in integrable and chaotic regimes at zero temperature. A clean Heisenberg chain with only nearest-neighbor interactions is integrable, whereas the addition of frustrating next-nearest neighbor interactions or yet of on-site disorder may lead to the onset of chaos. For a particular initial state far from equilibrium, the dynamics of local magnetization in the chaotic and non-chaotic clean chains is surprisingly similar, but differ significantly from the disordered system. We also discuss how quantum control methods consisting of sequences of magnetic pulses may be used to remove the effects of particular terms of the Hamiltonian, such as defects or unwanted interactions, and therefore induce a desired transport behavior.
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.