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  • Open Access

Topological Response in Open Quantum Systems with Weak Symmetries

Ze-Min Huang1, Sebastian Diehl1, and Xiao-Qi Sun2,3,*

  • *Contact author: xiaoqi.sun@mpq.mpg.de
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Phys. Rev. Lett. 135, 213002 – Published 20 November, 2025

DOI: https://doi.org/10.1103/qg2g-nz88

Abstract

In open quantum systems, the interaction of the system with its environment gives rise to two types of symmetry: a strong one, where the system’s symmetry charge is conserved exactly, and a weak one, where the system can exchange symmetry charge with the environment but still preserve symmetry at the ensemble level. While generic open quantum systems feature weak symmetries only, the symmetry-protected topological response for bosonic (spin) systems has only been considered in the stricter setup with additional strong symmetries. Here, we address the generic case and demonstrate that weak symmetries alone can protect topological responses that distinguish different phases of matter. For bosonic systems, focusing on one-dimensional mixed states described by locally purifiable density operators, we propose a quantized response characterizing qualitatively distinct phases. It is detectable via the decay behavior of different string order parameters. We illustrate our general results through a noisy Affleck-Kennedy-Lieb-Tasaki model. In particular, we show that the coupling to the environment can induce a phase transition to a state protected by weak symmetries, without a pure-state or strong-symmetry analog.

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Phys. Rev. Lett. 135, 213002– Published 20 November, 2025
  • Received 14 April 2025
  • Accepted 3 September 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

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