Hybrid Monte Carlo approach to the entanglement entropy of interacting fermions
Hybrid Monte Carlo approach to the entanglement entropy of interacting fermions
复制标题
混合蒙特卡罗方法计算相互作用费米子的纠缠熵
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
W. J. Porter
中科院分区：
文献类型：
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作者：
J. Drut;W. J. Porter
Monte Carlo方法计算相互作用费米子的R\'enyi纠缠熵S^{}_n存在一个著名的信噪比问题，即使在很多情况下也没有这个著名的符号问题.已经提出了一些方法来克服这个问题，如集成切换和使用辅助分区功能比。在这里，我们提出了一种方法，建立在最近提出的自由费米子分解方法;它采用纠缠的概率测度在一个自然的方式;它利用了混合蒙特卡罗算法（一个重要的工具，在晶格量子色动力学和其他规范理论与动态费米子）;它不受噪声问题。该方法与其他方法一样，在相同的情况下没有符号问题，因此适用于各种系统。作为原理的证明，我们计算了一维半满Hubbard模型的S_2 ^{}$，并与精确对角化和自由费米子分解方法的结果进行了比较。
The Monte Carlo calculation of R\'enyi entanglement entropies $S^{}_n$ of interacting fermions suffers from a well-known signal-to-noise problem, even for a large number of situations in which the infamous sign problem is absent. A few methods have been proposed to overcome this issue, such as ensemble switching and the use of auxiliary partition-function ratios. Here, we present an approach that builds on the recently proposed free-fermion decomposition method; it incorporates entanglement in the probability measure in a natural way; it takes advantage of the hybrid Monte Carlo algorithm (an essential tool in lattice quantum chromodynamics and other gauge theories with dynamical fermions); and it does not suffer from noise problems. This method displays no sign problem for the same cases as other approaches and is therefore useful for a wide variety of systems. As a proof of principle, we calculate $S_2^{}$ for the one-dimensional, half-filled Hubbard model and compare with results from exact diagonalization and the free-fermion decomposition method.