Dahlem Center for Complex Quantum Systems, Physics Department, Freie Universität Berlin, 14195 Berlin, Germany.
Institute of Physics, Johannes Gutenberg University, 55099 Mainz, Germany.
Phys Rev Lett. 2019 Feb 22;122(7):070502. doi: 10.1103/PhysRevLett.122.070502.
Tensor network methods have become a powerful class of tools to capture strongly correlated matter, but methods to capture the experimentally ubiquitous family of models at finite temperature beyond one spatial dimension are largely lacking. We introduce a tensor network algorithm able to simulate thermal states of two-dimensional quantum lattice systems in the thermodynamic limit. The method develops instances of projected entangled pair states and projected entangled pair operators for this purpose. It is the key feature of this algorithm to resemble the cooling down of the system from an infinite temperature state until it reaches the desired finite-temperature regime. As a benchmark, we study the finite-temperature phase transition of the Ising model on an infinite square lattice, for which we obtain remarkable agreement with the exact solution. We then turn to study the finite-temperature Bose-Hubbard model in the limits of two (hard-core) and three bosonic modes per site. Our technique can be used to support the experimental study of actual effectively two-dimensional materials in the laboratory, as well as to benchmark optical lattice quantum simulators with ultracold atoms.
张量网络方法已成为捕获强关联物质的强大工具，但在一维以上的有限温度下捕获实验中普遍存在的模型家族的方法在很大程度上仍然缺乏。我们引入了一种张量网络算法，能够在热力学极限下模拟二维量子晶格系统的热态。该方法为此目的开发了投影纠缠对态和投影纠缠对算符的实例。该算法的关键特点是类似于从无限温度状态冷却系统，直到达到所需的有限温度范围。作为基准，我们研究了无限正方形晶格上的伊辛模型的有限温度相变，我们得到了与精确解的显著一致性。然后，我们研究了每个站点具有两个（硬芯）和三个玻色子模式的有限温度玻色-哈伯德模型。我们的技术可用于支持实验室中实际有效的二维材料的实验研究，以及与超冷原子的光学晶格量子模拟器进行基准测试。
