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Universal Entanglement of Typical States in Constrained Systems
S C Morampudi1, A Chandran1, C R Laumann1
1Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
Physical Review Letters
|February 22, 2020
Summary
We developed a diagrammatic method to analyze entanglement in constrained quantum systems. This reveals universal phases and a critical point, with applications to spin chains and quantum defect models.
Area of Science:
- Quantum Information Science
- Condensed Matter Physics
Background:
- Entanglement dynamics are crucial in quantum systems.
- Understanding entanglement in constrained Hilbert spaces is challenging.
Purpose of the Study:
- To develop a method for evaluating entanglement spectra in large constrained Hilbert spaces.
- To classify entanglement spectra into universal phases based on singularities.
Main Methods:
- Diagrammatic formalism for exact evaluation.
- Analysis of random pure states in constrained Hilbert spaces.
- Classification of entanglement spectra based on singularities.
Main Results:
- Identified universal entanglement phases in constrained systems.
- Discovered a nontrivial phase diagram with a Marchenko-Pastur phase and a critical point.
- Proposed a quantum defect chain as a realization of the critical point.
- Showed that Rydberg-blockaded/Fibonacci chains exhibit a modified Page correction.
Conclusions:
- The developed formalism provides exact entanglement spectra for constrained quantum systems.
- The study reveals universal phase transitions and critical points in entanglement.
- Results predict and numerically confirm entanglement properties of thermalizing spin chains.
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