Quantum many-body topology in mixed quantum states

Symmetry-protected topological (SPT) phases have attracted significant attention in the field of condensed matter physics due to their remarkable properties, such as the presence of protected edge or surface modes. Although substantial progress has been made in understanding these phases in ideal, isolated systems at zero temperature, their behavior under non-ideal conditions involving quantum decoherence, or disorder presents a challenging area of study. In this talk, I will try to convey a new concept known as “averaged symmetry-protected topological phases” which is a natural generalization of SPT phases in open quantum systems. These phases exist within mixed ensembles where individual states break part of the protecting symmetry, but the symmetry is restored upon ensemble averaging. We will explore the physical properties and classification scheme for these unique phases. We will introduce the notion of “strange correlator” as a theoretical and numerical tool for detecting these phases.