Entanglement and Confinement in Coupled Quantum Systems

Abstract

We study some general properties of coupled quantum systems. We consider simple interactions between two copies of identical Hamiltonians such as the SYK model, Pauli spin chains with random magnetic field and harmonic oscillators. Such couplings make the ground states close to the thermofield double states of the uncoupled Hamiltonians. For the coupled SYK model, we push the numerical computation further towards the thermodynamic limit so that an extrapolation in the size of the system is possible. We find good agreement between the extrapolated numerical result and the analytic result in the large-$q$ limit. We also consider the coupled gauged matrix model and vector model, and argue that the deconfinement is associated with the loss of the entanglement, similarly to the previous observation for the coupled SYK model. The understanding of the microscopic mechanism of the confinement/deconfinement transition enables us to estimate the quantum entanglement precisely, and backs up the dual gravity interpretation which relates the deconfinement to the disappearance of the wormhole. Our results demonstrate the importance of the entanglement between the color degrees of freedom in the emergence of the bulk geometry from quantum field theory via holography.

32 pages, 13 figures. v2: published version

References in corpus (9)

• Many body localization and thermalization in quantum statistical mechanics
• Many-body localization edge in the random-field Heisenberg chain
• Entanglement as a Probe of Confinement
• Quantum chaos transition in a two-site SYK model dual to an eternal traversable wormhole
• How to Build the Thermofield Double State
• A proposal of the gauge theory description of the small Schwarzschild black hole in AdS${}_5\times$S${}^5$
• Anatomy of Deconfinement
• Entanglement Entropy of Two Coupled SYK Models and Eternal Traversable Wormhole
• Black Holes, Entanglement and Random Matrices

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• Spins-based Quantum Otto Engines and Majorisation
• Black holes Entangled by Radiation
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• Entanglement Entropy and Phase Space Density: Lowest Landau Levels and 1/2 BPS states
• Large N Optimization for multi-matrix systems
• Hamiltonian Forging of a Thermofield Double
• Random Circuits in the Black Hole Interior
• On SYK traversable wormhole with imperfectly correlated disorders
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• A bipartite Sachdev-Ye-Kitaev model: Conformal limit and level statistics
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