Condensed Matter Seminar

Speaker: Yizhi You, Professor, Department of Physics, Northeastern University Talk Title: Long-range order and symmetry breaking in mixed states triggered by local quantum channels Abstract: Any pure state that is reachable from a product state under a finite-depth unitary circuit is trivial in terms of its long-range order. However, mixed states can lose or gain long-range order under finite-depth quantum channels. The question of whether a mixed state possesses long-range order has a definite operational meaning. For example, in the toric code subjected to errors, logical information is retrievable if the error rate is below the error correction threshold. Nevertheless, the metrics proposed to diagnose mixed-state order involve manipulations of multiple copies of the mixed-state density matrix and lack a clear physical interpretation. We explore various mixed-state orders using the general framework of strong-to-weak symmetry breaking under finite-depth quantum channels. Our central finding is that the onset of long-range order in a mixed state at finite depth corresponds to the onset of symmetry-protected topological order in its purification picture. We will demonstrate that the Renyi-2 correlator, which captures the long-range order in the mixed state, can be traced back to the measurement-induced mutual information in the corresponding purified SPT state. Finally, we extend our discussion to mixed-state SPT and topological order and analyze their properties from the purification perspective.