时间矩阵乘积态理论及其应用

彭程; 冉仕举

doi:10.7523/j.issn.2095-6134.2019.06.004

中国科学院大学学报 >

2019 , Vol. 36 >Issue 6: 745 - 751

DOI: https://doi.org/10.7523/j.issn.2095-6134.2019.06.004

物理学

时间矩阵乘积态理论及其应用

彭程 ,
冉仕举

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1. 中国科学院大学物理科学学院, 北京 100049;
2. 西班牙光子科学研究所, 卡斯特利德费尔斯 08860

收稿日期: 2018-05-16

修回日期: 2018-05-28

网络出版日期: 2019-11-15

基金资助

国家自然科学基金（11574309）资助

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Time matrix product state: theory and applications

PENG Cheng ,
RAN Shiju

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1. School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;
2. ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels 08860, Spain

Received date: 2018-05-16

Revised date: 2018-05-28

Online published: 2019-11-15

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摘要

提出一种有效地刻画二维或高维量子临界系统的时间矩阵乘积态理论。利用数值重整化群，建立实空间矩阵乘积态与时间矩阵乘积态在描述高维量子多体系统的基态纠缠熵与关联长度两方面的等价性。在蜂窝状六角格子上的自旋1/2各向异性海森堡反铁磁模型中观察到两种不同类型的时间矩阵乘积态纠缠熵标度行为，还在kagome格子上的自旋1/2各向同性海森堡反铁磁体中观察到时间矩阵乘积态纠缠熵的对数型发散行为。这意味着高维量子系统的临界性有可能通过建立在一维时间矩阵乘积态基础上的（1+1）维共形场论来描述。

关键词： 量子临界; 纠缠熵; 关联长度; 标度律; 时间矩阵乘积态

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彭程 , 冉仕举 . 时间矩阵乘积态理论及其应用[J]. 中国科学院大学学报, 2019 , 36(6) : 745 -751 . DOI: 10.7523/j.issn.2095-6134.2019.06.004

Abstract

In this work, we propose an efficient approach to identify the criticality of finite-size quantum systems in higher-dimensions. Starting from the analysis of the numerical renormalization group flows, we build a general equivalence between the higher-dimensional ground state and an one-dimensional (1D) quantum state defined in the imaginary time direction in terms of the so-called time matrix product state (tMPS). We show that the criticality of the targeted model can be identified by the tMPS. We benchmark our proposal with the results obtained from the spin-1/2 Heisenberg antiferromagnet on honeycomb lattice. We also demonstrate critical scaling behavior of the tMPS on the spin-1/2 kagome Heisenberg antiferromagnet. The present study indicates that the 1D conformal field theory in the imaginary time provides a useful tool to characterize the criticality of higher-dimensional quantum systems.

Key words： criticality; entanglement entropy; correlation length; scaling law; time matrix product state

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