正则系综和量子数分布的矩阵乘积纯化
Matrix product purifications for canonical ensembles and quantum number distributions
摘要：
矩阵乘积纯化（MPPs）是模拟有限温度下强关联量子多体系统的一种非常有效的工具。当系统具有对称性时，这些可以用来大幅降低计算成本。计算巨正则系综的MPP是简单的，当利用对称性时也是如此。本文提供并证明了利用对称性有效计算正则系综MPPs的方法。此外，我们提出了一个计划的全球量子数分布的评估使用矩阵乘积密度算子（MPDO）。我们提供了精确的矩阵乘积表示的典型的无限温度状态，并讨论如何可以构建替代应用矩阵乘积算子真空型状态或使用纠缠哈密顿量。海森堡自旋1/2链的技术演示解释了为什么正则系综和巨正则系综的能量密度之差衰减为1/L。
英文摘要：
Matrix product purifications (MPPs) are a very efficient tool for the simulation of strongly correlated quantum many-body systems at finite temperatures. When a system features symmetries, these can be used to reduce computation costs substantially. It is straightforward to compute an MPP of a grand-canonical ensemble, also when symmetries are exploited. This paper provides and demonstrates methods for the efficient computation of MPPs of canonical ensembles under utilization of symmetries. Furthermore, we present a scheme for the evaluation of global quantum number distributions using matrix product density operators (MPDOs). We provide exact matrix product representations for canonical infinite-temperature states, and discuss how they can be constructed alternatively by applying matrix product operators to vacuum-type states or by using entangler Hamiltonians. A demonstration of the techniques for Heisenberg spin-1/2 chains explains why the difference in the energy densities of canonical and grand-canonical ensembles decays as 1/L.
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