Institute of Physics, Johannes Gutenberg University, 55099, Mainz, Germany.
Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstr. 2, 30167, Hannover, Germany.
Nat Commun. 2017 Nov 3;8(1):1291. doi: 10.1038/s41467-017-01511-6.
Understanding dissipation in 2D quantum many-body systems is an open challenge which has proven remarkably difficult. Here we show how numerical simulations for this problem are possible by means of a tensor network algorithm that approximates steady states of 2D quantum lattice dissipative systems in the thermodynamic limit. Our method is based on the intuition that strong dissipation kills quantum entanglement before it gets too large to handle. We test its validity by simulating a dissipative quantum Ising model, relevant for dissipative systems of interacting Rydberg atoms, and benchmark our simulations with a variational algorithm based on product and correlated states. Our results support the existence of a first order transition in this model, with no bistable region. We also simulate a dissipative spin 1/2 XYZ model, showing that there is no re-entrance of the ferromagnetic phase. Our method enables the computation of steady states in 2D quantum lattice systems.
理解二维量子多体系统的耗散是一个悬而未决的问题，证明非常困难。在这里，我们展示了如何通过张量网络算法来实现这一问题的数值模拟，该算法在热力学极限下近似二维量子格耗散系统的稳态。我们的方法基于这样一种直觉，即强耗散在量子纠缠变得太大而无法处理之前就将其杀死。我们通过模拟耗散量子伊辛模型来验证其有效性，该模型与相互作用的里德堡原子耗散系统有关，并通过基于乘积和相关态的变分算法对我们的模拟进行基准测试。我们的结果支持该模型存在一级相变，没有双稳区。我们还模拟了耗散自旋 1/2 XYZ 模型，表明铁磁相没有再进入。我们的方法使二维量子格系统中稳态的计算成为可能。
