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

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。 我们将建立在最近的进展领域的量子场蒙特卡罗模拟的费米子系统，允许计算的纠缠哈密顿量的频谱，甚至哈密顿量本身。 这个量可能会引起极大的兴趣，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。

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.