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Reviews in Mathematical Physics

Enhanced Binding in a General Class of Quantum Field Models

Asao Arai, Hiroyuki Kawano

Published Jun 1, 2003• 33 citations
Publisher

Abstract

We consider, in an abstract form, a system of "quantum particles" coupled to a Bose field. It is shown that, under suitable hypotheses, the composed system can have a ground state even if the uncoupled particle system has no ground state.
DOI
10.1142/s0129055x03001680

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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-qlimit. 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.
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