标题： 纠缠与负号问题之间的相关性 显示英文标题

标题： On the correlation between entanglement and the negative sign problem

摘要： 在本工作中，我们研究了在低维强关联量子多体系统模拟中，量子蒙特卡罗方法中纠缠与负号问题之间的相关性。 纠缠熵表征了使用张量网络状态相关方法进行多体模拟的难度，而平均符号则衡量了多种量子蒙特卡罗方法进行多体模拟的难度。 尽管存在某些情况下某种方法优于另一种方法，但为了在计算复杂性方面对一般的困难强关联系统找到纠缠与平均符号之间可能的相关性，这是有必要的。 我们以掺杂二维Hubbard模型为例，并数值计算了基态中通过密度矩阵重整化群得到的纠缠以及低温下辅助场量子蒙特卡罗模拟中的平均符号的掺杂演化。 结果表明它们确实存在相关性。 纠缠熵（平均符号）在20%掺杂附近显示出峰值（谷值），表明这是两种方法的困难区域。 20%掺杂附近也是Hubbard模型和铜氧化物高温超导体中最引人注目的区域，在这里能量相近的竞争态相互交织。 认识到纠缠与平均符号之间的相关性为理解强关联量子多体系统模拟的难度提供了新的见解。 显示英文摘要

摘要： In this work, we study the correlation between entanglement and the negative sign problem in quantum Monte Carlo for the simulation of low-dimensional strongly correlated quantum many body systems. Entanglement entropy characterizes the difficulty of many-body simulation with tensor network state related methods, while the average sign measures the difficulty in many-body simulation for a variety of quantum Monte Carlo methods. Although there exist cases where one type of method works better than the other, it is desirable to find the possible correlation between entanglement and average sign for general hard strongly correlated systems regarding computational complexity. We take the doped two-dimensional Hubbard model as an example and numerically calculate the doping evolution of both the entanglement in the ground state with Density Matrix Renormalization Group and the average sign in the Auxiliary Field Quantum Monte Carlo simulation at low temperature. The results show that they are indeed correlated. The entanglement entropy (average sign) shows a peak (dip) around 20% doping, indicating that it is the difficult region for both methods. The vicinity of 20% doping is also the most intriguing region in both the Hubbard model and cuprate high-Tc superconductors where competing states with close energy intertwine with each other. Recognizing the correlation between entanglement and average sign provides new insight into our understanding of the difficulty in the simulation of strongly correlated quantum many-body systems.