On SYK traversable wormhole with imperfectly correlated disorders

DOI10.1007/JHEP04(2023)145arXiv2210.13123OpenAlexW4367854064MaRDI QIDQ6105705

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Publication date: 9 June 2023

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Abstract: In this paper we study the phase structure of two Sachdev-Ye-Kitaev models (L-system and R-system) coupled by a simple interaction, with imperfectly correlated disorder. When the disorder of the two systems are perfectly correlated, $J_{i_{1}cdots{i}_q}^{(L)}=J_{i_{1}cdots{i}_q}^{(R)}$, this model is known to exhibit a phase transition at a finite temperature between the two-black hole phase at high-temperature and the traversable wormhole phase at low temperature. We find that, as the correlation $langle{J}_{i_{1}cdots{i}_q}^{(L)}{J}_{i_{1}cdots{i}_q}^{(R)}angle$ is decreased, the critical temperature becomes lower. At the same time, the transmission between L-system and R-system in the low-temperature phase becomes more suppressed, while the chaos exponent of the whole system becomes larger. Interestingly we also observe that when the correlation is smaller than some q-dependent critical value the phase transition completely disappears in the entire parameter space. At zero temperature, the energy gap becomes larger as we decrease the correlation. We also use a generalized thermofield double state as a variational state. Interestingly, this state coincide with the ground state in the large q limit.

Full work available at URL: https://arxiv.org/abs/2210.13123

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