Schwarzian correction to quantum correlation in SYK model

TL;DR

This paper analytically investigates quantum corrections in SYK-type models via Schwarzian action, revealing strong correlation signatures and quantum chaos through density of states modifications and out-of-time order correlations.

Contribution

It provides an analytical study of Schwarzian corrections in SYK models from a gravity dual perspective, connecting quantum chaos and strong correlation effects.

Findings

Quantum correction causes transfer of spectral weight from quasiparticle peak to Hubbard band.

Higher order OTOCs exhibit Lyapunov exponent, indicating quantum chaos.

Local spin-spin correlations relate to dynamical susceptibility in quantum liquids.

Abstract

We study a class of SYK-type models in large N limit from the gravity dual side in terms of Schwarzian action analytically. The quantum correction to two point correlation function due to the Schwarzian action produces transfer of degree of freedom from the quasiparticle peak to 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 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 spin glasses, disordered metals.