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Measurement-Induced Phase Transition in the Monitored Sachdev-Ye-Kitaev Model
Shao-Kai Jian1, Chunxiao Liu2, Xiao Chen3
1Condensed Matter Theory Center and Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20742, USA.
Physical Review Letters
|October 15, 2021
Summary
We study entanglement phase transitions in monitored Sachdev-Ye-Kitaev (SYK) chains. A key finding is that varying measurement rates can break symmetries, altering entanglement entropy scaling from area-law to log-scaling or volume-law.
Area of Science:
- Quantum Information Theory
- Condensed Matter Physics
- High Energy Physics
Background:
- The Sachdev-Ye-Kitaev (SYK) model describes quantum chaotic systems.
- Continuous monitoring introduces quantum trajectories and can drive phase transitions.
- Entanglement entropy scaling reveals critical properties of quantum many-body systems.
Purpose of the Study:
- To investigate entanglement phase transitions in monitored Brownian SYK chains.
- To analytically derive the effective action and understand the role of symmetry breaking.
- To characterize the different entanglement entropy scaling behaviors in various phases.
Main Methods:
- Analytical derivation of the effective action in the large-N limit.
- Exploration of symmetry breaking in an enlarged replica space.
- Numerical verification of critical exponents using Schwinger-Dyson equations.
Main Results:
- An entanglement transition is driven by symmetry breaking in the replica space.
- Non-interacting SYK2 chains exhibit O(2) symmetry breaking, leading to log-scaling entanglement entropy (vortices) or area-law scaling.
- Interacting SYK chains show C4 symmetry breaking, resulting in volume-law entanglement entropy due to domain wall costs.
Conclusions:
- Continuous monitoring of SYK chains can induce distinct entanglement phases.
- Symmetry breaking in replica space is the mechanism behind these entanglement transitions.
- The nature of the symmetry (continuous vs. discrete) dictates the resulting entanglement scaling laws.
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