Beyond quantum cluster theories: multiscale approaches for strongly correlated systems
Beyond quantum cluster theories: multiscale approaches for strongly correlated systems
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超越量子簇理论：强相关系统的多尺度方法
DOI：
10.1088/2058-9565/ac676b
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发表时间：
2022
影响因子：
6.7
通讯作者：
Moreno, Juana
中科院分区：
文献类型：
--
作者：
Fotso, Herbert F;Tam, Ka-Ming;Moreno, Juana
赋予强关联系统许多有趣性质的自由度，也使它们通过典型的微扰处理变得相当棘手。出于这个原因，负责其技术上有前途的特性的机制仍然大多难以捉摸。计算方法在填补这一空白的努力中发挥了重要作用。特别是，动力学平均场理论和它的集群扩展，动力学集群近似允许重大进展。然而，尽管这些嵌入方案的所有有见地的结果，计算约束，如量子蒙特卡罗（QMC）中的负号问题，和希尔伯特空间的指数增长的精确对角化（艾德）的方法，仍然限制了长度范围内的相关性，可以在形式主义的处理。最近的一个进步，旨在克服这些困难是多尺度的许多机构的方法的发展，从而解决这一挑战，通过引入一个中间的长度尺度之间的短长度尺度的相关性被视为完全使用集群求解器，如QMC或艾德，和长的长度尺度的相关性被视为在平均场的方式。在这个中间长度尺度上，相关性可以用微扰的方法来处理。这是多尺度多体方法的本质。我们将回顾这些多尺度多体方法的各种实现，它们所产生的结果，以及为进一步发展而应解决的突出挑战。
The degrees of freedom that confer to strongly correlated systems their many intriguing properties also render them fairly intractable through typical perturbative treatments. For this reason, the mechanisms responsible for their technologically promising properties remain mostly elusive. Computational approaches have played a major role in efforts to fill this void. In particular, dynamical mean field theory and its cluster extension, the dynamical cluster approximation have allowed significant progress. However, despite all the insightful results of these embedding schemes, computational constraints, such as the minus sign problem in quantum Monte Carlo (QMC), and the exponential growth of the Hilbert space in exact diagonalization (ED) methods, still limit the length scale within which correlations can be treated exactly in the formalism. A recent advance aiming to overcome these difficulties is the development of multiscale many body approaches whereby this challenge is addressed by introducing an intermediate length scale between the short length scale where correlations are treated exactly using a cluster solver such QMC or ED, and the long length scale where correlations are treated in a mean field manner. At this intermediate length scale correlations can be treated perturbatively. This is the essence of multiscale many-body methods. We will review various implementations of these multiscale many-body approaches, the results they have produced, and the outstanding challenges that should be addressed for further advances.
DOI：
10.1143/ptps.176.117
发表时间：
2008
期刊：
arXiv: Strongly Correlated Electrons
影响因子：
--
作者：
K. Held;A. Katanin;A. Toschi
通讯作者：
A. Toschi