论文标题
费米子 - 丙烷和交替的基本量子量蒙特卡洛方法，用于晶格上的相关电子
Fermionic-propagator and alternating-basis quantum Monte Carlo methods for correlated electrons on a lattice
论文作者
论文摘要
哈伯德模型的Ultrocold-Atom模拟提供了对电荷特征和旋转相关性的见解。另一方面，相应的数值模拟仍然是一个重大挑战。我们基于连续空间中电子的量子蒙特卡洛（QMC）模拟的最新进展，并将相似的想法应用于方形哈伯德模型。我们设计和基准测试了两种离散时间QMC方法，即费米子 - 丙烷QMC（FPQMC）和交替的基本基础QMC（ABQMC）。在FPQMC中，时间的演变由真实空间中的快照表示，而ABQMC中的快照在真实空间和相互空间之间交替。这些方法可以应用于研究大型典型或规范合奏中的平衡特性，外部野外淬火，甚至纯状态的演变。各种真实空间/相互空间相关功能也在其范围内。两种方法都涉及大小的矩阵等于粒子数量（因此与轨道或时间切片的数量无关），这允许廉价更新。我们在相关设置中基准测试方法。在平衡中，发现FPQMC方法具有出色的平均符号，在某些情况下，即使假想时间离散化较差，也会产生正确的结果。 ABQMC的平均迹象明显较差，但也会产生良好的结果。出于平衡，FPQMC遭受了强大的动态标志问题。相反，在ABQMC中，符号问题不是时间依赖。使用ABQMC，我们计算几种实验相关纯状态的生存概率。
Ultracold-atom simulations of the Hubbard model provide insights into the character of charge and spin correlations in and out of equilibrium. The corresponding numerical simulations, on the other hand, remain a significant challenge. We build on recent progress in the quantum Monte Carlo (QMC) simulation of electrons in continuous space, and apply similar ideas to the square-lattice Hubbard model. We devise and benchmark two discrete-time QMC methods, namely the fermionic-propagator QMC (FPQMC) and the alternating-basis QMC (ABQMC). In FPQMC, the time evolution is represented by snapshots in real space, whereas the snapshots in ABQMC alternate between real and reciprocal space. The methods may be applied to study equilibrium properties within grand-canonical or canonical ensemble, external field quenches, and even the evolution of pure states. Various real-space/reciprocal-space correlation functions are also within their reach. Both methods deal with matrices of size equal to the number of particles (thus independent of the number of orbitals or time slices), which allows for cheap updates. We benchmark the methods in relevant setups. In equilibrium, the FPQMC method is found to have excellent average sign and, in some cases, yields correct results even with poor imaginary-time discretization. ABQMC has significantly worse average sign, but also produces good results. Out of equilibrium, FPQMC suffers from a strong dynamical sign problem. On the contrary, in ABQMC, the sign problem is not time dependent. Using ABQMC, we compute survival probabilities for several experimentally relevant pure states.
