Classification of topological phases in one dimensional interacting non-Hermitian systems and emergent unitarity

一维有相互作用系统中拓扑相的分类与演生幺正性

Topological phases in non-Hermitian systems have become fascinating subjects recently.In this paper,we attempt to classify topological phases in 1D interacting non-Hermitian systems.We begin with the non-Hermitian generalization of the Su-Schrieffer-Heeger(SSH)model and discuss its many-body topological Berry phase,which is well defined for all interacting quasi-Hermitian systems(non-Hermitian systems that have real energy spectrum).We then demonstrate that the classification of topological phases for quasi-Hermitian systems is exactly the same as their Hermitian counterparts.Finally,we construct the fixed point partition function for generic 1D interacting non-Hermitian local systems and find that the fixed point partition function still has a one-to-one correspondence to their Hermitian counterparts.Thus,we conclude that the classification of topological phases for generic 1D interacting non-Hermitian systems is still exactly the same as Hermitian systems.

近年来,非厄米系统中的拓扑相是一个重要的研究热点.本文尝试分类一维有相互作用非厄米系统中的拓扑相.首先,作者将SSH模型推广到了非厄米情形,并详细讨论该模型的拓扑多体贝里相位.在准厄米系统(能谱为实数的非厄米系统)中,多体贝里相位是具备良好定义的.之后,该工作展示对于准厄米系统,其拓扑分类与厄米情况是相同的.最后,对于一般性的一维有相互作用非厄米系统,该工作构造了它们的不动点配分函数,并且发现这些不动点配分函数仍然与厄米系统的不动点配分函数有着一一对应.因此,可以得出结论,即对于一般性的一维有相互作用非厄米系统,其拓扑分类与厄米情况是相同的.