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arXiv · 1810.04157

Universal entanglement of typical states in constrained systems

Siddhardh C. Morampudi·Anushya Chandran·Chris R. Laumann
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Abstract

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, $ΔS_1 = 0.513595\cdots$. Our results predict the entanglement of infinite temperature eigenstates in thermalizing constrained systems and provide a baseline for numerical studies.

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Siddhardh C. Morampudi, Anushya Chandran, Chris R. Laumann. 2018-10-09. Universal entanglement of typical states in constrained systems. https://doi.org/10.1103/physrevlett.124.050602

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