Precise evaluation of thermal response functions by optimized density matrix renormalization group schemes
Precise evaluation of thermal response functions by optimized density matrix renormalization group schemes
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DOI：
10.1088/1367-2630/15/7/073010
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发表时间：
2013-01
影响因子：
3.3
通讯作者：
T. Barthel
中科院分区：
文献类型：
--
作者：
T. Barthel
本文提供了一个研究和讨论的早期，以及新的更有效的计划，精确评估的有限温度响应函数的强关联量子系统的框架内的时间依赖的密度矩阵重整化群（tDMRG）。以自旋为1/2的XXZ海森堡链为例，研究了临界XY相和带隙的Néel相的计算代价和键尺寸随时间和温度的变化.算法中的矩阵乘积状态净化与相应的矩阵乘积算子是一一对应的。这种符号简化阐明了准局域性对计算成本的影响。基于在有限温度下设计有效的tDMRG格式来计算动态耗散子的观察结果，对最近在Barthel，Schollwöck和Sachdev（2012 arXiv：1212.3570）中提出的一类新的可优化格式进行了解释和数值分析。一个特定的新的接近最优的方案，不需要额外的优化达到最大的时间，通常增加了2倍，与早期的方法相比。这些增加的可访问时间使更多的物理应用程序可访问。对于所描述的tDMRG方案中的每一个，可以设计对应的传输矩阵重整化群变体。
This paper provides a study and discussion of earlier as well as novel more efficient schemes for the precise evaluation of finite-temperature response functions of strongly correlated quantum systems in the framework of the time-dependent density matrix renormalization group (tDMRG). The computational costs and bond dimensions as functions of time and temperature are examined for the example of the spin-1/2 XXZ Heisenberg chain in the critical XY phase and the gapped Néel phase. The matrix product state purifications occurring in the algorithms are in a one-to-one relation with the corresponding matrix product operators. This notational simplification elucidates implications of quasi-locality on the computational costs. Based on the observation that there is considerable freedom in designing efficient tDMRG schemes for the calculation of dynamical correlators at finite temperatures, a new class of optimizable schemes, as recently suggested in Barthel, Schollwöck and Sachdev (2012 arXiv:1212.3570), is explained and analyzed numerically. A specific novel near-optimal scheme that requires no additional optimization reaches maximum times that are typically increased by a factor of 2, when compared against earlier approaches. These increased reachable times make many more physical applications accessible. For each of the described tDMRG schemes, one can devise a corresponding transfer matrix renormalization group variant.