Correlation functions in Schwarzian liquid

Abstract

We analytically study low-temperature universal properties of a class of SYK-type models in the large N limit from the AdS2 gravity dual side in terms of SL(2,R)-invariant Schwarzian action. The quantum correction to the conformal field theory CFT1 two-point correlation function due to the Schwarzian action produces a transfer of degree of freedom from the quasiparticle peak to the Hubbard band in density of states (DOS), a signature strong correlation. In Schwinger-Keldysh (SK) formalism, we calculate higher-point thermal out-of-time order correlation (OTOC) functions, which indicate quantum chaos by having a Lyapunov exponent. Higher-order local spin-spin correlations are also calculated, which can be related to the dynamical local susceptibility of quantum liquids such as the spin liquid in disordered metals, marginal Fermi liquid, non-Fermi liquid, etc.