标题： 融合矩阵乘积态与量子蒙特卡罗方法：同时减少纠缠和符号问题 显示英文标题

标题： Fusing matrix-product states with quantum Monte Carlo: reducing entanglement and sign problem at the same time

摘要： 关联量子物质系统对任何可能的求解方法都是一个严峻的挑战。基于矩阵乘积态（MPS）的方法可以准精确地描述一维系统，但往往难以保留足够的双部分纠缠来准确近似二维系统。相反，基于采样概率分布的量子蒙特卡洛（QMC）方法通常可以以采样规模增大而系统性地减少误差的方式近似二维和三维系统。然而，QMC可能会遭受所谓的符号问题，这使得该方法对于许多感兴趣的系统来说成本过高，例如在非共格密度下相互排斥的费米子系统和受挫系统。在本文中，我们介绍了一种新的混合方法，该方法结合了辅助场量子蒙特卡洛（AFQMC）与基于MPS的算法。这种混合技术可以消除或减轻符号问题（取决于具体模型），同时需要保留的双部分纠缠远低于直接应用MPS算法所需的水平，且不需要使用不受控制的近似。我们展示了该算法的两个应用场景，这些场景用其他任何方法都难以或无法解决，并量化了剩余符号问题的程度。 显示英文摘要

摘要： Systems of correlated quantum matter can be a steep challenge to any would-be method of solution. Matrix-product state (MPS)-based methods can describe 1D systems quasiexactly, but often struggle to retain sufficient bipartite entanglement to accurately approximate 2D systems already. Conversely, Quantum Monte Carlo (QMC) approaches, based on sampling a probability distribution, can generally approximate 2D and 3D systems with an error that decays systematically with growing sampling size. However, QMC can suffer from the so-called sign problem, that makes the approach prohibitively costly for many systems of interest, such as repulsively interacting fermions away from commensurate densities and frustrated systems. In this article, we introduce a new hybrid approach, that combines auxiliary-field QMC (AFQMC) with MPS-based algorithms. This hybrid technique removes or reduces the sign problem (depending on the specific model) while also needing to retain much lower bipartite entanglement than brute-force application of a MPS-algorithm, without the use of uncontrolled approximations. We present two use-cases of the algorithm that would be challenging or impossible to address with any other approach, and quantify the extent of any remaining sign problem.