Being able to accurately describe the dynamics steady states of driven and/or dissipative but quantum correlated lattice models is of fundamental importance in many areas of science: from quantum information to biology. An efficient numerical simulation of large open systems in two spatial dimensions is a challenge. In this work, we develop a tensor network method, based on an infinite projected entangled pair operator ansatz, applicable directly in the thermodynamic limit. We incorporate techniques of finding optimal truncations of enlarged network bonds by optimizing an objective function appropriate for open systems. Comparisons with numerically exact calculations, both for the dynamics and the steady state, demonstrate the power of the method. In particular, we consider dissipative transverse quantum Ising, driven-dissipative hard-core boson, and dissipative anisotropic $XY$ models in non-mean-field limits, proving able to capture substantial entanglement in the presence of dissipation. Our method enables us to study regimes that are accessible to current experiments but lie well beyond the applicability of existing techniques.

中文翻译：

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二维开放量子格子模型动力学的稳定iPEPO张量网络算法

在从量子信息到生物学的许多科学领域中，能够准确描述驱动和/或耗散但与量子相关的晶格模型的动力学稳态至关重要。在两个空间维度上对大型开放系统进行有效的数值模拟是一个挑战。在这项工作中，我们开发了基于无限投影纠缠对算子ansatz的张量网络方法，该方法直接适用于热力学极限。我们结合了通过优化适用于开放系统的目标函数来找到扩大的网络键的最佳截断的技术。与动力学和稳态数值精确计算的比较证明了该方法的强大功能。特别是，我们考虑了耗散横向量子伊辛，驱动耗散硬核玻色子，$Xÿ$非平均场限制下的模型，证明能够在存在耗散的情况下捕获大量纠缠。我们的方法使我们能够研究可用于当前实验的方案，但远远超出了现有技术的适用范围。