On SYK traversable wormhole with imperfectly correlated disorders

Abstract

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 is perfectly correlated, $$ {J}_{i_1\cdots {i}_q}^{(L)}={J}_{i_1\cdots {i}_q}^{(R)} $$ J i 1 ⋯ i q L = J i 1 ⋯ 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 $$ \left\langle {J}_{i_1\cdots {i}_q}^{(L)}={J}_{i_1\cdots {i}_q}^{(R)}\right\rangle $$ J i 1 ⋯ i q L = J i 1 ⋯ i q R is decreased, the critical temperature becomes lower. At the same time, the transmission between the 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 coincides with the ground state in the large q limit.