Dissipative Symmetry-Protected Topological Order

TL;DR

This paper explores how dissipation affects symmetry-protected topological order in a quantum spin chain, showing that certain topological features persist in steady states under symmetric dissipation, expanding understanding of topological phases in open systems.

Contribution

It demonstrates that symmetry-protected topological order can survive in mixed states under Markovian dissipation, providing a new perspective on topological phases in open quantum systems.

Findings

Topological signatures persist in steady states with time-reversal symmetric dissipation.

Finite string-order parameters indicate topological order in mixed states.

Non-symmetric dissipation destroys the topological features.

Abstract

In this work, we investigate the interplay between dissipation and symmetry-protected topological order. We considered the one-dimensional spin-1 Affleck-Kennedy-Lieb-Tasaki model interacting with an environment where the dissipative dynamics are described by the Lindladian master equation. The Markovian dynamics is solved by the implementation of a tensor network algorithm for mixed states in the thermodynamic limit. We observe that, for time-reversal symmetric dissipation, the resulting steady state has topological signatures even if being a mixed state. This is seen in finite string-order parameters as well as in the degeneracy pattern of singular values in the tensor network decomposition of the reduced density matrix. We also show that such features do not appear for non-symmetric dissipation. Our work opens the way toward a generalized and more practical definition of symmetry-protected topological order for mixed states induced by dissipation.