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

TL;DR

This paper introduces an inequality involving Rényi-2 correlators that helps diagnose strong-weak spontaneous symmetry breaking in fermionic open quantum systems, revealing decoherence's role in driving symmetry breaking.

Contribution

The paper establishes a new inequality for Rényi-2 correlators that bounds the decohered fermionic state, linking decoherence to symmetry breaking diagnostics in quantum matter.

Findings

Inequality bounds Rényi-2 correlators for decohered fermions.

Decoherence promotes U(1) spontaneous symmetry breaking.

Connections made to quantum spin Hall and Dirac spin liquids.

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.