Strong-to-weak Symmetry Breaking and Entanglement Transitions

Abstract

When interacting with an environment, the entanglement within quantum many-body systems is rapidly transferred to the entanglement between the system and the bath. For systems with a large local Hilbert space dimension, this leads to a first-order entanglement transition for the reduced density matrix of the system. On the other hand, recent studies have introduced a new paradigm for classifying density matrices, with particular focus on scenarios where a strongly symmetric density matrix undergoes spontaneous symmetry breaking to a weak symmetry phase. This is typically characterized by a finite Rényi-2 correlator or a finite Wightman correlator. In this work, we study the entanglement transition from the perspective of strong-to-weak symmetry breaking, using solvable complex Brownian SYK models. We perform analytical calculations for both the early-time and late-time saddles. The results show that while the Rényi-2 correlator indicates a transition from symmetric to symmetry-broken phase, the Wightman correlator becomes finite even in the early-time saddle due to the single-replica limit, demonstrating that the first-order transition occurs between a near-symmetric phase and a deeply symmetry-broken phase in the sense of Wightman correlator. Our results provide a novel viewpoint on the entanglement transition under symmetry constraints and can be readily generalized to systems with repeated measurements.

7 pages, 1 figure

References in corpus (23)

• Logical quantum processor based on reconfigurable atom arrays
• High-fidelity parallel entangling gates on a neutral atom quantum computer
• Quantum Optimization of Maximum Independent Set using Rydberg Atom Arrays
• Controlling many-body dynamics with driven quantum scars in Rydberg atom arrays
• Critical properties of the measurement-induced transition in random quantum circuits
• High-fidelity gates with mid-circuit erasure conversion in a metastable neutral atom qubit
• Quantum criticality under decoherence or weak measurement
• Multi-qubit gates and Schrödinger cat states in an optical clock
• How to Build the Thermofield Double State
• Lindbladian dissipation of strongly-correlated quantum matter
• Lindbladian dynamics of the Sachdev-Ye-Kitaev model
• Scrambling Transition in a Radiative Random Unitary Circuit
• High-fidelity detection of large-scale atom arrays in an optical lattice
• Unifying Emergent Hydrodynamics and Lindbladian Low Energy Spectra across Symmetries, Constraints, and Long-Range Interactions
• Dynamical quantum phase transitions in SYK Lindbladians
• Keldysh Wormholes and Anomalous Relaxation in the Dissipative Sachdev-Ye-Kitaev Model
• Dynamical Transition of Operator Size Growth in Quantum Systems Embedded in an Environment
• Note on entropy dynamics in the Brownian SYK model
• Information Scrambling and Entanglement Dynamics of Complex Brownian Sachdev-Ye-Kitaev Models
• Entanglement Phases in large-N hybrid Brownian circuits with long-range couplings
• Strong-to-weak symmetry breaking states in stochastic dephasing stabilizer circuits
• Symmetries as Ground States of Local Superoperators: Hydrodynamic Implications
• Entanglement Transition and Replica Wormhole in the Dissipative Sachdev-Ye-Kitaev Model

Cited by in corpus (6)

• Scheme to Detect the Strong-to-weak Symmetry Breaking via Randomized Measurements
• Exactly solvable dissipative dynamics and one-form strong-to-weak spontaneous symmetry breaking in interacting two-dimensional spin systems
• Quantum Strong-to-Weak Spontaneous Symmetry Breaking in Decohered One Dimensional Critical States
• Dissipation- versus Chaos-Induced Relaxation in Non-Markovian Quantum Many-Body Systems
• Noisy Monitored Quantum Circuits
• Robust Mixed-State Cluster States and Spurious Topological Entanglement Negativity