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arXiv · 2603.24671

Inequality for Strong-Weak Spontaneous Symmetry Breaking in Fermionic Open Quantum systems

Abhijat Sarma·Cenke Xu
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Abstract

Under decoherence, an initial Gaussian (free-fermion) state evolves into a non-Gaussian mixed state, so the resulting decohered fermionic state is not exactly solvable in general. We show through an inequality that a class of R\'{e}nyi-2 correlators of the decohered fermion state are upper-bounded by the R\'{e}nyi-2 correlator serving as a proximate diagnostic of strong-weak spontaneous symmetry breaking (SW-SSB) of the charge-U(1) symmetry. This inequality holds for arbitrary decoherence strength and suggests that decoherence drives fermionic quantum matter toward U(1) SW-SSB. We also make connections between our inequality and other subjects such as projected quantum spin Hall insulator and Dirac spin liquid states.

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Abhijat Sarma, Cenke Xu. 2026-03-25. Inequality for Strong-Weak Spontaneous Symmetry Breaking in Fermionic Open Quantum systems. https://arxiv.org/abs/2603.24671

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