Algebraic Relaxation of Strong-to-Weak Symmetry-Breaking Order via Charge-Sector Broadening
Abstract
Strong-to-weak spontaneous symmetry breaking (SW-SSB) is a distinctive phenomenon of mixed quantum states, characterized by nonlinear long-range order associated with strong symmetry. In realistic open quantum systems, however, strong symmetry is macroscopically fragile and can be explicitly reduced to weak symmetry through local charge exchange with the environment. In this paper, we investigate how the SW-SSB order decays under such strong-symmetry-breaking Liouvillian dynamics. For discrete ℤ2 symmetry, a local symmetry-breaking perturbation drives an exponential decay of the Rényi-1 long-range correlator, revealing the fragility of discrete SW-SSB order. By contrast, for continuous U(1) symmetry, local charge exchange broadens the distribution over symmetry-charge sectors and leads to parametrically slower algebraic relaxation. We establish a rigorous algebraic lower bound on the connected Rényi-1 long-range correlation, demonstrating the robustness of this slow relaxation. In the thermodynamic limit, we further uncover a two-stage dynamical scaling: R̃1∼ t−1 at early times and R̃1∼ t−1/z at long times, with z set by the underlying hydrodynamic dynamics. As a numerical verification, we consider fermionic chains with z=2 and z=4, which are excellent agreement with the theoretical predictions.
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BibTeX
@misc{fang2026algebraic,
title = {{Algebraic Relaxation of Strong-to-Weak Symmetry-Breaking Order via Charge-Sector Broadening}},
author = {Zi-Xi Fang and Kai Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00474},
eprint = {2610.00474},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00474},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Algebraic Relaxation of Strong-to-Weak Symmetry-Breaking Order via Charge-Sector Broadening
AU - Zi-Xi Fang
AU - Kai Zhang
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00474
UR - https://arxiv.org/abs/2610.00474
AB - Strong-to-weak spontaneous symmetry breaking (SW-SSB) is a distinctive phenomenon of mixed quantum states, characterized by nonlinear long-range order associated with strong symmetry. In realistic open quantum systems, however, strong symmetry is macroscopically fragile and can be explicitly reduced to weak symmetry through local charge exchange with the environment. In this paper, we investigate how the SW-SSB order decays under such strong-symmetry-breaking Liouvillian dynamics. For discrete ℤ_2 symmetry, a local symmetry-breaking perturbation drives an exponential decay of the Rényi-1 long-range correlator, revealing the fragility of discrete SW-SSB order. By contrast, for continuous U(1) symmetry, local charge exchange broadens the distribution over symmetry-charge sectors and leads to parametrically slower algebraic relaxation. We establish a rigorous algebraic lower bound on the connected Rényi-1 long-range correlation, demonstrating the robustness of this slow relaxation. In the thermodynamic limit, we further uncover a two-stage dynamical scaling: R̃_1∼ t^−1 at early times and R̃_1∼ t^−1/z at long times, with z set by the underlying hydrodynamic dynamics. As a numerical verification, we consider fermionic chains with z=2 and z=4, which are excellent agreement with the theoretical predictions.
ER -