有限温度量子多体系统与热态张量网络

Finite-temperature quantum many-body systems and thermal tensor networks

量子多体系统热力学性质的精确模拟在理论和实验方面都具有重要的价值。局域相互作用量子多体系统的热态满足互信息(mutual information)面积律,对于这样的系统,热态张量网络可以提供满足面积律的精确"波函数"拟设,提供了模拟有限温度系统的有力手段。文章介绍了关联格点模型在有限温度下的热态张量网络刻画及相关模拟方法。作者按照世界线热态张量网络和级数展开热态张量网络来分别介绍,并讨论了自由能极小变分原理与重正化群剪裁的优化原则。世界线框架内,人们发展了转移矩阵重正化群,基于纯化策略的有限温度密度矩阵重正化群,以及张量网络的线性重正化群等方法。在此基础上,介绍作者新近提出的级数展开热态张量网络方法,该方法受随机级数展开量子蒙特卡罗方法的启发,突破了世界线方法的局限,提高了有限温度计算重正化群模拟的精度标准,并且在计算阻挫量子自旋链模型时不会有负符号问题。此外,文章讨论了在两维格点系统上推广有限温度张量网络计算的进展和未来展望。

Thermal states of quantum lattice models, which are of great interest both theo- retically and experimentally, satisfy an area law of mutual information. Thermal tensor networks could provide an efficient representation for thermal states in the quantum many-body systems with local interactions. Renormalization group （RG） methods based on the world-line Trotter-Suzuki decomposition, including the transfer-matrix RG and finite-temperature density-matrix RG, constitute an important class of thermal tensor network methods. On the other hand, inspired by the stochastic series expansion （SSE） quantum Monte Carlo method, recently we developed a series-expansion thermal tensor network （SETTN） method realizing an RG thermal calculation in essentially continuous time and therefore with no discretization error. Furthermore, unlike the SSE method, SETTN does not suffer from the notorious negative sign problem. Besides one- dimensional cases, we also discuss two possible routes, i.e., the matrix-product and the tensor- product operators, to generalize the thermal tensor network algorithms to two dimensions.