Entanglement entropies and spectra of interacting fermions from quantum Monte Carlo simulations

量子蒙特卡罗模拟中相互作用的费米子的纠缠熵和光谱

• 批准号: 299339031
• 负责人: Professor Dr. Fakher Fakhry Assaad
• 金额: --
• 依托单位: Lehrstuhl für Theoretische Physik I - Festkörperphysik
• 依托单位国家: 德国
• 项目类别: Research Units
• 财政年份: 2016
• 资助国家: 德国
• 起止时间: 2015-12-31 至 2020-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/299339031?language=en
• 关键词: Entanglement; entropies; spectra; interacting; fermions

In this grant proposal we will consider strongly-correlated many body quantum systems from the point of view of entanglement. To define entanglement one can consider a ground state wave function of a d-dimensional system and carry out a real space bipartition. Integrating out half of the space produces a mixed state described by a reduced density matrix. The negative logarithm of this reduced density matrix corresponds to the entanglement Hamiltonian and its entropy to the entropy of entanglement. We will build on recent progress in the realm of auxiliary-field quantum Monte Carlo simulations for fermionic systems which allow the calculation of the spectrum of the entanglement Hamiltonian or even of the Hamiltonian itself. This quantity is potentially of great interest since its form is very often dictated by global or emergent symmetries. It is also a tool of choice to characterize topological states of matter. With our novel numerical tools we will seek to compute the entanglement Hamiltonian at finite and zero temperature for a variety of problems, including one-dimensional correlated electron models, spin systems across quantum critical points, and topological phases of matter. Being a stochastic method, and for the class of problems where the infamous sign problem is absent, the numerical complexity of our approach scales polynomially with system size and inverse temperature.

在这个资助计划中，我们将从纠缠的角度考虑强关联的多体量子系统。 为了定义纠缠，可以考虑d维系统的基态波函数，并进行真实的空间二分。积分出一半的空间产生由约化密度矩阵描述的混合状态。这个约化密度矩阵的负对数对应于纠缠哈密顿量，其熵对应于纠缠熵。 我们将在费米子系统辅助场量子蒙特卡罗模拟领域的最新进展的基础上再接再厉，该模拟允许计算纠缠汉密尔顿量甚至汉密尔顿量本身的谱。 这个量可能会引起人们的极大兴趣，因为它的形式通常由全局对称性或突现对称性决定。它也是描述物质拓扑状态的工具。 利用我们新颖的数值工具，我们将寻求计算各种问题在有限和零温度下的纠缠哈密顿量，包括一维相关电子模型，跨量子临界点的自旋系统和物质的拓扑相。作为一种随机方法，对于一类不存在臭名昭著的符号问题的问题，我们的方法的数值复杂性与系统大小和逆温度成多项式关系。