Multiscale Space-Time Ansatz for Correlation Functions of Quantum Systems Based on Quantics Tensor Trains
Multiscale Space-Time Ansatz for Correlation Functions of Quantum Systems Based on Quantics Tensor Trains
复制标题
DOI：
10.1103/physrevx.13.021015
复制
发表时间：
2022-10
影响因子：
12.5
通讯作者：
H. Shinaoka;M. Wallerberger;Y. Murakami;Kosuke Nogaki;Rihito Sakurai;P. Werner;A. Kauch
中科院分区：
文献类型：
--
作者：
H. Shinaoka;M. Wallerberger;Y. Murakami;Kosuke Nogaki;Rihito Sakurai;P. Werner;A. Kauch
量子系统的相关函数是量子场论中的中心对象，在高维时空域中定义。因此，它们的数值处理受到维度的诅咒，这阻碍了复杂的多体理论在有趣问题上的应用。在这里，我们提出了一个基于量子张量序列（QTT）的量子系统相关函数的多尺度时空ansatz，“量子比特”描述了指数不同的长度尺度。然后，ansatz通过将得到的高维张量分解为张量列（也称为矩阵积态）来假设长度尺度的分离。我们对各种平衡和非平衡系统进行了数值验证，并在具有挑战性的情况下展示了几个数量级的压缩率。图解方程的基本组成部分，如卷积或傅立叶变换，都是以压缩形式表述的。我们在数值上证明了所提出的方法对Dyson方程和Bethe-Salpeter方程的稳定性和有效性。{QTT表示}为实现量子场论的高效计算提供了一个统一的框架。
Correlation functions of quantum systems -- central objects in quantum field theories -- are defined in high-dimensional space-time domains. Their numerical treatment thus suffers from the curse of dimensionality, which hinders the application of sophisticated many-body theories to interesting problems. Here, we propose a multi-scale space-time ansatz for correlation functions of quantum systems based on quantics tensor trains (QTT), ``qubits'' describing exponentially different length scales. The ansatz then assumes a separation of length scales by decomposing the resulting high-dimensional tensors into tensor trains (known also as matrix product states). We numerically verify the ansatz for various equilibrium and nonequilibrium systems and demonstrate compression rates of several orders of magnitude for challenging cases. Essential building blocks of diagrammatic equations, such as convolutions or Fourier transforms are formulated in the compressed form. We numerically demonstrate the stability and efficiency of the proposed methods for the Dyson and Bethe-Salpeter equations. {The QTT representation} provides a unified framework for implementing efficient computations of quantum field theories.