Universal entanglement of typical states in constrained systems

Local constraints play an important role in the effective description of many quantum systems. Their impact on dynamics and entanglement thermalization are just beginning to be unravelled. We develop a large \(N\) diagrammatic formalism to exactly evaluate the bipartite entanglement of random pure s...

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Bibliographic Details
Published in:arXiv.org 2018-10
Main Authors: Morampudi, Siddhardh C, Chandran, Anushya, Laumann, Chris R
Format: Article
Language:English
Subjects:
Constraints
Critical point
Eigenvectors
Entanglement
Hilbert space
Phase diagrams
Singularities
System effectiveness
Thermalization (energy absorption)
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Summary:Local constraints play an important role in the effective description of many quantum systems. Their impact on dynamics and entanglement thermalization are just beginning to be unravelled. We develop a large \(N\) diagrammatic formalism to exactly evaluate the bipartite entanglement of random pure states in large constrained Hilbert spaces. The resulting entanglement spectra may be classified into `phases' depending on their singularities. Our closed solution for the spectra in the simplest class of constraints reveals a non-trivial phase diagram with a Marchenko-Pastur (MP) phase which terminates in a critical point with new singularities. The much studied Rydberg-blockaded/Fibonacci chain lies in the MP phase with a modified Page correction to the entanglement entropy, \(\Delta S_1 = 0.513595\cdots\). Our results predict the entanglement of infinite temperature eigenstates in thermalizing constrained systems and provide a baseline for numerical studies.
ISSN:2331-8422
DOI:10.48550/arxiv.1810.04157