Strong-to-weak spontaneous symmetry breaking meets average symmetry-protected topological order

Abstract

Recent studies have unveiled new possibilities for discovering intrinsic quantum phases that are unique to open systems, including phases with average symmetry-protected topological (ASPT) order and strong-to-weak spontaneous symmetry breaking (SWSSB) order in systems with global symmetry. In this work, we propose a new class of phases, termed the double ASPT phase, which emerges from a nontrivial extension of these two orders. This new phase is absent from prior studies and cannot exist in conventional closed systems. Using the recently developed imaginary-Lindbladian formalism, we explore the phase diagram of a one-dimensional open system with ${\mathbb{Z}}_2^{\sigma }\times {\mathbb{Z}}_2^{\tau }$ symmetry. We identify universal critical behaviors along each critical line and observe the emergence of an intermediate phase that completely breaks the ${\mathbb{Z}}_2^{\sigma }$ symmetry, leading to the formation of two triple points in the phase diagram. These two triple points are topologically distinct and connected by a domain-wall decoration duality map. Our results promote the establishment of a complete classification for quantum phases in open systems with various symmetry conditions.

13 pages, 9 figures, to appear in Phys. Rev. B as a Letter

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Cited by in corpus (7)

• Scheme to Detect the Strong-to-weak Symmetry Breaking via Randomized Measurements
• Observation of average topological phase in disordered Rydberg atom array
• Gauge theory and mixed state criticality
• A New Framework for Quantum Phases in Open Systems: Steady State of Imaginary-Time Lindbladian Evolution
• Boundary anomaly detection in two-dimensional subsystem symmetry-protected topological phases
• Exactly solvable dissipative dynamics and one-form strong-to-weak spontaneous symmetry breaking in interacting two-dimensional spin systems
• Noisy Monitored Quantum Circuits