In mixed quantum states, the notion of symmetry is divided into two types: strong and weak symmetry. While spontaneous symmetry breaking (SSB) for a weak symmetry is detected by two-point correlation functions, SSB for a strong symmetry is characterized by the Rényi-2 correlators. In this work we present a way to construct various SSB phases for strong symmetries, starting from the ground state phase diagram of lattice gauge theory models. In addition to introducing a type of mixed-state topological phases, we provide models of the criticalities between them, including those with gapless symmetry-protected topological order. We clarify that the ground states of lattice gauge theories are purified states of the corresponding mixed SSB states. Our construction can be applied to any finite gauge theory and offers a framework to study quantum operations between mixed quantum phases.

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• Gauge theories
• Open quantum systems
• Quantum criticality
• Spontaneous symmetry breaking
• Symmetry protected topological states