非平衡定态的纠缠结构
Entanglement structure of non-equilibrium steady states
摘要：
我们研究了计算相互作用量子系统的输运性质的问题，特别是电导率和热导率，通过计算由接触偏置的系统的非平衡稳态（NESS）。我们的方法是基于在NESS纠缠的结构。通过合理的物理假设，我们证明了接近局部平衡的NESS是轻度纠缠的，并且可以通过计算高效的张量网络来表示。我们进一步认为，可以通过在多种适当的低纠缠态中动态演化系统来找到NESS。一个物理上现实的动力学演化定律是马尔可夫开放系统动力学，或称林德布拉德方程。我们探索这种方法在一个研究充分的自由费米子模型与文献的比较是可能的。我们研究了有无无序的电流和热流，并计算了互信息和条件互信息等熵量。最后，我们讨论了这种方法的前景具有挑战性的问题，在强相互作用的系统，特别是那些无序的运输。
英文摘要：
We study the problem of calculating transport properties of interacting quantum systems, specifically electrical and thermal conductivities, by computing the non-equilibrium steady state (NESS) of the system biased by contacts. Our approach is based on the structure of entanglement in the NESS. With reasonable physical assumptions, we show that a NESS close to local equilibrium is lightly entangled and can be represented via a computationally efficient tensor network. We further argue that the NESS may be found by dynamically evolving the system within a manifold of appropriate low entanglement states. A physically realistic law of dynamical evolution is Markovian open system dynamics, or the Lindblad equation. We explore this approach in a well-studied free fermion model where comparisons with the literature are possible. We study both electrical and thermal currents with and without disorder, and compute entropic quantities such as mutual information and conditional mutual information. We conclude with a discussion of the prospects of this approach for the challenging problem of transport in strongly interacting systems, especially those with disorder.
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