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.
Highlights
Prescriptions useful for theoretical considerations and experimental studies
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
When the quantum theory admits a dual gravity description, the thermofield double state (TFD) state is dual to the eternal black hole, which is a maximally entangled black hole connected by the Einstein-Rosen bridge [2, 3]
Summary
As a concrete example of a coupled Hamiltonian (1.2), we consider the coupled SYK models [10] by taking. It is possible to identify the deviation from unit overlap with the possible 1/q corrections that one has to take into account in the large-q analysis [10] It is argued in [10] that such a deviation is due to the possible excitations due to the stronger left-right coupling to the coupled model so that it is not accurate to mimic the ground state of the coupled system as the TFD state at some temperature.. We observe that in the same range of values of μ where we could extrapolate the q = 4 data, the dependence of β(μ) on N is not always monotonous: for the very small set of data that we have access currently, β(μ) tends to first increase with N (in the opposite direction than the one expected from the analytical prediction), and it tends to decrease again for larger N Note that this effect is hardly visible on the scale of figure 2.
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