摘要 (Abstract) ：

Symmetry plays a central role in characterizing quantum phases. In open quantum systems, it arises in two distinct forms: weak symmetry, where charges are conserved only on average, and strong symmetry, with exact conservation laws. In this talk, I will explore their physical implications in 1D open systems using a tensor network framework. For weak symmetry, I will show that it enables a quantized response distinguishing mixed-state phases, including those without pure-state analogs, identifiable through string order parameters. For strong symmetry, I construct a broad class of renormalization fixed-point mixed states that exhibit zero correlation length and anomalous symmetry. Despite the absence of local correlations, these states cannot be efficiently prepared, indicating intrinsic long-range entanglement.

References:

[1] ZM Huang, S Diehl, XQ Sun，Phys. Rev. Lett. 135, 213002 (2025)

[2] XQ Sun, arXiv:2504.16985Top of Form