Emergent Replica Conformal Symmetry in Non-Hermitian SYK${}_2$ Chains

Abstract

Recently, the steady states of non-unitary free fermion dynamics are found to exhibit novel critical phases with power-law squared correlations and a logarithmic subsystem entanglement. In this work, we theoretically understand the underlying physics by constructing solvable static/Brownian quadratic Sachdev-Ye-Kitaev chains with non-Hermitian dynamics. We find the action of the replicated system generally shows (one or infinite copies of) $O(2)\times O(2)$ symmetries, which is broken to $O(2)$ by the saddle-point solution. This leads to an emergent conformal field theory of the Goldstone modes. We derive the effective action and obtain the universal critical behaviors of squared correlators. Furthermore, the entanglement entropy of a subsystem $A$ with length $L_A$ corresponds to the energy of the half-vortex pair $S\sim {\rho }_s\log L_A$, where ${\rho }_s$ is the total stiffness of the Goldstone modes. We also discuss special limits with more than one branch of Goldstone modes and comment on interaction effects.

16 pages, 4 figures

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• Symmetry of Open Quantum Systems: Classification of Dissipative Quantum Chaos
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• Controlling entanglement at absorbing state phase transitions in random circuits
• Lindbladian dissipation of strongly-correlated quantum matter
• Disordered monitored free fermions
• Lindbladian dynamics of the Sachdev-Ye-Kitaev model
• Universal Entanglement Transitions of Free Fermions with Long-range Non-unitary Dynamics
• Dynamics of measured many-body quantum chaotic systems
• Purification Timescales in Monitored Fermions
• Volume-law to area-law entanglement transition in a non-unitary periodic Gaussian circuit
• Non-Hermitian skin effect in one-dimensional interacting Bose gas
• Dynamical quantum phase transitions in SYK Lindbladians
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• Keldysh Wormholes and Anomalous Relaxation in the Dissipative Sachdev-Ye-Kitaev Model
• Measurement-induced phase transitions in sparse nonlocal scramblers
• Universality and its limits in non-Hermitian many-body quantum chaos using the Sachdev-Ye-Kitaev model
• Multifractality in non-unitary random dynamics
• Information Scrambling and Entanglement Dynamics of Complex Brownian Sachdev-Ye-Kitaev Models
• Density and current statistics in boundary-driven monitored fermionic chains
• Emergent Symmetry in Brownian SYK Models and Charge Dependent Scrambling
• Entanglement Transition and Replica Wormhole in the Dissipative Sachdev-Ye-Kitaev Model
• Universal Properties of the Spectral Form Factor in Open Quantum Systems
• Distinguishing Quantum Phases through Cusps in Full Counting Statistics
• Singular Value Decomposition and Its Blind Spot for Quantum Chaos in Non-Hermitian Sachdev-Ye-Kitaev Models
• Gapless Symmetry-Protected Topological States in Measurement-Only Circuits
• Strong-to-weak Symmetry Breaking and Entanglement Transitions
• Spacetime picture for entanglement generation in noisy fermion chains
• Quantum chaos in the Dicke model and its variants
• Unveiling Eigenstate Thermalization for Non-Hermitian systems
• Universal hard-edge statistics of non-Hermitian random matrices
• Measurement-Induced Phase Transition in State Estimation of Chaotic Systems and the Directed Polymer
• Tunable Geometries in Sparse Clifford Circuits
• Defect conformal field theory from Sachdev-Ye-Kitaev interactions
• Current Correlations and Conductivity in SYK-Like Systems: An Analytical Study
• Euclidean-to-Lorentzian wormhole transition and gravitational symmetry breaking in the Sachdev-Ye-Kitaev model