Wójtowicz Gabriela, Elenewski Justin E, Rams Marek M, Zwolak Michael
Jagiellonian University, Institute of Theoretical Physics, Lojasiewicza 11, 30-348 Kraków, Poland.
Biophysics Group, Microsystems and Nanotechnology Division, Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD, USA.
Phys Rev A (Coll Park). 2020;101. doi: 10.1103/PhysRevA.101.050301.
Tensor networks are a powerful tool for many-body ground states with limited entanglement. These methods can nonetheless fail for certain time-dependent processes-such as quantum transport or quenches-where entanglement growth is linear in time. Matrix-product-state decompositions of the resulting out-of-equilibrium states require a bond dimension that grows exponentially, imposing a hard limit on simulation timescales. However, in the case of transport, if the reservoir modes of a closed system are arranged according to their scattering structure, the entanglement growth can be made logarithmic. Here, we apply this ansatz to open systems via extended reservoirs that have explicit relaxation. This enables transport calculations that can access steady states, time dynamics and noise, and periodic driving (e.g., Floquet states). We demonstrate the approach by calculating the transport characteristics of an open, interacting system. These results open a path to scalable and numerically systematic many-body transport calculations with tensor networks.
张量网络是研究具有有限纠缠的多体基态的强大工具。然而，对于某些随时间变化的过程，如量子输运或猝灭，这些方法可能会失效，在这些过程中纠缠随时间呈线性增长。对产生的非平衡态进行矩阵乘积态分解需要一个指数增长的键维度，这对模拟时间尺度施加了严格限制。然而，在输运的情况下，如果一个封闭系统的库模式根据其散射结构排列，纠缠增长可以是对数形式的。在这里，我们通过具有明确弛豫的扩展库将这种假设应用于开放系统。这使得输运计算能够访问稳态、时间动力学和噪声以及周期性驱动（例如弗洛凯态）。我们通过计算一个开放相互作用系统的输运特性来演示该方法。这些结果为使用张量网络进行可扩展且数值系统的多体输运计算开辟了一条道路。
