Minimally entangled typical thermal states versus matrix product purifications for the simulation of equilibrium states and time evolution
Minimally entangled typical thermal states versus matrix product purifications for the simulation of equilibrium states and time evolution
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DOI：
10.1103/physrevb.92.125119
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发表时间：
2014-11
影响因子：
3.7
通讯作者：
M. Binder;T. Barthel
中科院分区：
文献类型：
--
作者：
M. Binder;T. Barthel
为了模拟强相关量子多体系统的平衡态和有限温度响应函数，我们比较了密度矩阵重整化群（DMRG）框架下两种不同方法的效率。第一种是基于矩阵产品的纯化。第二个，也是最近的一个，是基于所谓的最小纠缠典型热态（METTS）。对于后者，我们强调了统计和DMRG截断误差的相互作用，讨论了自平均效应的使用，并描述了响应函数的计算方案。对于自旋-1/2 XXZ链的临界相和间隙相以及一维玻色-哈伯德模型，我们评估了两种方法在不同温度下的计算成本和精度。对于几乎所有考虑的情况，我们发现，对于相同的计算成本，净化产生比METTS更准确的结果——通常是数量级上的。METTS算法只有在远低于系统能量缺口的温度下才更有效。响应函数评估中计算成本的指数增长限制了两种方法可达到的时间尺度，我们发现在这方面，METTS并不优于净化。
For the simulation of equilibrium states and finite-temperature response functions of strongly-correlated quantum many-body systems, we compare the efficiencies of two different approaches in the framework of the density matrix renormalization group (DMRG). The first is based on matrix product purifications. The second, more recent one, is based on so-called minimally entangled typical thermal states (METTS). For the latter, we highlight the interplay of statistical and DMRG truncation errors, discuss the use of self-averaging effects, and describe schemes for the computation of response functions. For critical as well as gapped phases of the spin-1/2 XXZ chain and the one-dimensional Bose-Hubbard model, we assess computation costs and accuracies of the two methods at different temperatures. For almost all considered cases, we find that, for the same computation cost, purifications yield more accurate results than METTS -- often by orders of magnitude. The METTS algorithm becomes more efficient only for temperatures well below the system's energy gap. The exponential growth of the computation cost in the evaluation of response functions limits the attainable timescales in both methods and we find that in this regard, METTS do not outperform purifications.