Entanglement and confinement in coupled quantum systems

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