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arXiv:1303.6353 · Journal of Statistical Mechanics Theory and Experiment

Heat transport in the X X Z spin chain: from ballistic to diffusive regimes and dephasing enhancement

Juan José Mendoza-Arenas, Sarah Al-Assam, Stephen R. L. Clark, Dieter Jaksch

Published Jul 16, 2013• 79 citations
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Abstract

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.

DOI
10.1088/1742-5468/2013/07/p07007

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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.
Abstract The Lindblad dynamics with dephasing in the bulk and magnetization-driving at the two boundaries is studied for the quantum spin chain with random fields h j and couplings J j (that can be either uniform or random). In the regime of strong disorder in the random fields, or in the regime of strong bulk-dephasing, the effective dynamics can be mapped onto a classical simple symmetric exclusion process with quenched disorder in the diffusion coefficient associated to each bond. The properties of the corresponding non-equilibrium-steady-state in each disordered sample between the two reservoirs are studied in detail by extending the methods that have been previously developed for the symmetric exclusion process without disorder. Explicit results are given for the magnetization profile, for the two-point correlations, for the mean current and for the current fluctuations, in terms of the random fields and couplings defining the disordered sample.
Abstract We study the non-equilibrium transport properties of a highly anisotropic two-dimensional lattice of particles governed by a Heisenberg XXZ Hamiltonian. The anisotropy of the lattice allows us to approximate the system at finite temperature as an array of incoherently coupled one-dimensional chains. We show that in the regime of strong intrachain interactions, the weak interchain coupling considerably boosts spin transport in the driven system. Interestingly, we show that this enhancement increases with the length of the chains, which is related to superdiffusive spin transport. We describe the mechanism behind this effect, compare it to a similar phenomenon in single chains induced by dephasing, and explain why the former is much stronger.
In this work, we study the transport properties of the anisotropic Heisenberg model in a disordered magnetic field and in the presence of dephasing due to external degrees of freedom. Without dephasing, the model can display, depending on parameter values, the whole range of possible transport regimes: ideal ballistic conduction, diffusive, or ideal insulating behavior. We show that the presence of dephasing induces normal diffusive transport in a wide range of parameters. We also analyze the dependence of spin conductivity on the dephasing strength. In addition, by analyzing the decay of the spin–spin correlation function, we find a long-range order for finite chain sizes. All our results for a one-dimensional spin chain at infinite temperature can be equivalently rephrased for strongly interacting disordered spinless fermions.
Non-equilibrium spin-chain systems have been attracting increasing interest in energy transport. This work studies a one-dimensional non-equilibrium Ising chain immersed in a tilted magnetic field, where every spin contacts a Boson reservoir with the dissipative system-environment interaction. We analytically investigate the dynamics and the steady-state energy transport taking advantage of the Born-Markov-secular master equation. In the longitudinal field, one can find that the non-dissipative N' spins decompose the spin chain into N' + 1 independent subchains and block the heat currents from the hot end to the cool end. Moreover, for the non-dissipative μth spin, its nearest two bulk spins become the nodal spins in the subchains and have the corresponding energy correction of ±Jμ-1,μ and ±Jμ,μ+1 depending on the excited/ground state of the μth spin. Therefore, a magnetically controlled heat modulator can be designed by adjusting the direction of the magnetic field in which the non-dissipative spin is located. For the transverse field case, the whole Hilbert space of the chain can always be divided into two independent subspaces regardless of whether the bulk spin is dissipative. This work provides new insight into the dynamics and energy transport of the dissipative Ising model.
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.
We study the non-equilibrium transport properties of a highly anisotropic two-dimensional lattice of particles governed by a Heisenberg XXZ Hamiltonian. The anisotropy of the lattice allows us to approximate the system at finite temperature as an array of incoherently coupled one-dimensional chains. We show that in the regime of strong intrachain interactions, the weak interchain coupling considerably boosts spin transport in the driven system. Interestingly, we show that this enhancement increases with the length of the chains, which is related to superdiffusive spin transport. We describe the mechanism behind this effect, compare it to a similar phenomenon in single chains induced by dephasing, and explain why the former is much stronger.