On SYK traversable wormhole with imperfectly correlated disorders

TL;DR

This paper investigates how imperfect disorder correlation affects the phase transition and properties of coupled SYK models, revealing suppression of the traversable wormhole phase and changes in chaos and energy gap.

Contribution

It introduces analysis of the phase structure of coupled SYK models with imperfect disorder correlation, showing how correlation influences phase transition and system properties.

Findings

Critical temperature decreases with less disorder correlation.

Transmission between systems is suppressed at low temperatures with lower correlation.

Phase transition disappears below a q-dependent critical correlation.

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 $\langle J_{i_1\cdots i_q}^{(L)} J_{i_1\cdots i_q}^{(R)}\rangle$ 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.