时间矩阵乘积态理论及其应用

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。

Time matrix product state: theory and applications

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.