用张量网络克服Monte Carlo符号问题
Towards overcoming the Monte Carlo sign problem with tensor networks
摘要：
格点规范理论的蒙特卡罗模拟研究受到在某些情况下，特别是在非零化学势下出现的臭名昭著的符号问题的阻碍。到目前为止，还没有通用的方法来克服这个问题。然而，近年来出现了一类新的非微扰哈密顿技术，称为张量网络，其中没有符号问题。在以前的工作中，我们已经证明，这种方法，特别是在1+1维矩阵乘积态，可以用来执行精确的计算在格点规范理论，无质量和大量的Schwinger模型。我们已经计算了这个理论的质谱，它的热性质和实时动力学。在这项工作中，我们回顾这些结果，我们扩展我们的计算的情况下，两种口味和非零化学势。我们能够可靠地再现已知的分析结果，这个模型，从而表明，张量网络可以解决的格点规范理论在有限密度的符号问题。
英文摘要：
The study of lattice gauge theories with Monte Carlo simulations is hindered by the infamous sign problem that appears under certain circumstances, in particular at non-zero chemical potential. So far, there is no universal method to overcome this problem. However, recent years brought a new class of non-perturbative Hamiltonian techniques named tensor networks, where the sign problem is absent. In previous work, we have demonstrated that this approach, in particular matrix product states in 1+1 dimensions, can be used to perform precise calculations in a lattice gauge theory, the massless and massive Schwinger model. We have computed the mass spectrum of this theory, its thermal properties and real-time dynamics. In this work, we review these results and we extend our calculations to the case of two flavours and non-zero chemical potential. We are able to reliably reproduce known analytical results for this model, thus demonstrating that tensor networks can tackle the sign problem of a lattice gauge theory at finite density.
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