Instability of steady-state mixed-state symmetry-protected topological order to strong-to-weak spontaneous symmetry breaking
Abstract
Recent experimental progress in controlling open quantum systems enables the pursuit of mixed-
state nonequilibrium quantum phases. We investigate whether open quantum systems hosting
mixed-state symmetry-protected topological states as steady states retain this property under sym-
metric perturbations. Focusing on the decohered cluster state—a mixed-state symmetry-protected
topological state protected by a combined strong and weak symmetry—we construct a parent Lind-
bladian that hosts it as a steady state. This Lindbladian can be mapped onto exactly solvable
reaction-diffusion dynamics, even in the presence of certain perturbations, allowing us to solve the
parent Lindbladian in detail and reveal previously-unknown steady states. Using both analytical
and numerical methods, we find that typical symmetric perturbations cause strong-to-weak sponta-
neous symmetry breaking at arbitrarily small perturbations, destabilize the steady-state mixed-state
symmetry-protected topological order. However, when perturbations introduce only weak symmetry
defects, the steady-state mixed-state symmetry-protected topological order remains stable. Addi-
tionally, we construct a quantum channel which replicates the essential physics of the Lindbladian
and can be efficiently simulated using only Clifford gates, Pauli measurements, and feedback.
state nonequilibrium quantum phases. We investigate whether open quantum systems hosting
mixed-state symmetry-protected topological states as steady states retain this property under sym-
metric perturbations. Focusing on the decohered cluster state—a mixed-state symmetry-protected
topological state protected by a combined strong and weak symmetry—we construct a parent Lind-
bladian that hosts it as a steady state. This Lindbladian can be mapped onto exactly solvable
reaction-diffusion dynamics, even in the presence of certain perturbations, allowing us to solve the
parent Lindbladian in detail and reveal previously-unknown steady states. Using both analytical
and numerical methods, we find that typical symmetric perturbations cause strong-to-weak sponta-
neous symmetry breaking at arbitrarily small perturbations, destabilize the steady-state mixed-state
symmetry-protected topological order. However, when perturbations introduce only weak symmetry
defects, the steady-state mixed-state symmetry-protected topological order remains stable. Addi-
tionally, we construct a quantum channel which replicates the essential physics of the Lindbladian
and can be efficiently simulated using only Clifford gates, Pauli measurements, and feedback.
