量子蒙特卡罗方法测量Berry曲率
Measuring Berry curvature with quantum Monte Carlo
摘要：
Berry曲率和它的后代Berry相位在量子力学中起着重要的作用。它们可以用来理解Aharonov-Bohm效应，定义拓扑Chern数，并通常用于研究量子基态流形的几何性质。虽然Berry曲率已经在少体物理和非相互作用粒子的制度得到了很好的研究，它的使用在强相互作用的制度是阻碍了缺乏数值方法来解决it. In本文中，我们填补了这一空白，通过实施量子Monte Carlo方法来解决Berry曲率的基础上解释Berry曲率作为一个领先的校正虚时间斜坡。我们证明了我们的算法使用横向场伊辛模型在一个和两个维度，后者是不可积的。尽管事实上，Berry曲率的波函数的相位信息，我们表明，我们的算法没有符号或相位问题的标准符号问题的自由哈密顿。我们的算法规模类似于传统的方法作为系统的大小和能隙的函数，因此应该证明是一个有价值的工具，在调查的量子几何多体系统。
英文摘要：
The Berry curvature and its descendant, the Berry phase, play an important role in quantum mechanics. They can be used to understand the Aharonov-Bohm effect, define topological Chern numbers, and generally to investigate the geometric properties of a quantum ground state manifold. While Berry curvature has been well-studied in the regimes of few-body physics and non-interacting particles, its use in the regime of strong interactions is hindered by the lack of numerical methods to solve it. In this paper we fill this gap by implementing a quantum Monte Carlo method to solve for the Berry curvature, based on interpreting Berry curvature as a leading correction to imaginary time ramps. We demonstrate our algorithm using the transverse-field Ising model in one and two dimensions, the latter of which is non-integrable. Despite the fact that the Berry curvature gives information about the phase of the wave function, we show that our algorithm has no sign or phase problem for standard sign-problem-free Hamiltonians. Our algorithm scales similarly to conventional methods as a function of system size and energy gap, and therefore should prove a valuable tool in investigating the quantum geometry of many-body systems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
