Strong-to-weak symmetry breaking states in stochastic dephasing stabilizer circuits

Abstract

Discovering mixed state quantum orders is an on-going issue. Recently, it has been recognized that there are (at least) two kinds of symmetries in the mixed state; strong and weak symmetries. Under symmetry-respective decoherence, spontaneous strong-to-weak symmetry breaking (SSSB) can occur. This work provides a scheme to describe SSSB and other decoherence phenomena in the mixed state by employing the stabilizer formalism and the efficient numerical algorithm of Clifford circuits. We present two systematic numerical studies.In a two-dimensional (2D) circuit with a stochastic Ising type decoherence, an SSSB phase transition is clearly observed and its criticality is elucidated by the numerical methods. In particular, we calculate Rényi-2 correlations and estimate critical exponents of the SSSB transition. For the second system, we introduce an idea of subgroup SSSB. As an example, we study a system with symmetry-protected-topological (SPT) order provided by both one-form and zero-form symmetries, and observe how the system evolves under decoherence. After displaying numerical results, we show that viewpoint of percolation is quite useful to understand the SSSB transition, which is applicable for a wide range of decohered states. Finally, we comment on SSSB of one-form-symmetry exemplifying toric code.

13 pages, 4 figures. Accepted to Phys. Rev. B

References in corpus (20)

• Generalized Global Symmetries
• Generalized Symmetries in Condensed Matter
• Quantum criticality under decoherence or weak measurement
• Long-range entanglement from measuring symmetry-protected topological phases
• Measurement-Induced Power-Law Negativity in an Open Monitored Quantum Circuit
• Mixed-state long-range order and criticality from measurement and feedback
• Topology, criticality, and dynamically generated qubits in a stochastic measurement-only Kitaev model
• Pivot Hamiltonians as generators of symmetry and entanglement
• Symmetry protection of measurement-based quantum computation in ground states
• Separability transitions in topological states induced by local decoherence
• Topological order and entanglement dynamics in the measurement-only XZZX quantum code
• Quantum spin systems for measurement-based quantum computation
• Detecting and stabilizing measurement-induced symmetry-protected topological phases in generalized cluster models
• Measurement-induced phase transitions in the toric code
• Production of lattice gauge-Higgs topological states in measurement-only quantum circuit
• Bulk-Measurement-Induced Boundary Phase Transition in Toric Code and Gauge-Higgs Model
• Phase transition and evidence of fast-scrambling phase in measurement-only quantum circuit
• Measurement-only dynamical phase transition of topological and boundary order in toric code and gauge-Higgs models
• Hierarchy of emergent cluster states by measurement from symmetry-protected-topological states with large symmetry to subsystem cat state
• Stabilization of symmetry-protected long-range entanglement in stochastic quantum circuits

Cited by in corpus (14)

• Strong-to-weak spontaneous symmetry breaking meets average symmetry-protected topological order
• Efficient Detection of Strong-To-Weak Spontaneous Symmetry Breaking via the Rényi-1 Correlator
• Strong and weak symmetries and their spontaneous symmetry breaking in mixed states emerging from the quantum Ising model under multiple decoherence
• Strong-to-weak Symmetry Breaking and Entanglement Transitions
• Intrinsic mixed state topological order in a stabilizer system under stochastic decoherence: Strong-to-weak spontaneous symmetry breaking from percolation point of view
• Mixed-state phase transitions in spin-Holstein models
• Scheme to Detect the Strong-to-weak Symmetry Breaking via Randomized Measurements
• Gauge theory and mixed state criticality
• Hardness of observing strong-to-weak symmetry breaking
• Many-body quantum catalysts for transforming between phases of matter
• Quantum Strong-to-Weak Spontaneous Symmetry Breaking in Decohered One Dimensional Critical States
• Measurement-only circuit of perturbed toric code on triangular lattice: Topological entanglement, 1-form symmetry and logical qubits
• Instability of steady-state mixed-state symmetry-protected topological order to strong-to-weak spontaneous symmetry breaking
• Robust Mixed-State Cluster States and Spurious Topological Entanglement Negativity