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.
Highlights
The second one is the emergence of conformal symmetry at the IR limit, as well as its spontaneous breaking which results in soft modes as the pseudo Nambu-Goldstone bosons [7,23,33]
In this paper, motivated by the novel features of the spin liquid phase in SY state [2,38] in disordered metals depicted by SYK-like models [39,40,41], we study a general class of strongly interacting (0 þ 1)-dimensional quantum mechanical models in the large N limit [16], whose lowenergy dynamics is depicted by the Schwarzian action
In the SYK model, the emergent Diff 1 symmetry is explicitly broken, since the symmetry is not kept by the Lagrangian any more as one slightly moves away from the IR conformal fixed point, where the kinetic term ∂ τ becomes relevant at low frequency or strong coupling region (ω ≪ 1 or J ≫ 1)
Summary
Attracted a lot of interest [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37]. In this paper, motivated by the novel features of the spin liquid phase in SY state [2,38] in disordered metals depicted by SYK-like models [39,40,41], we study a general class of strongly interacting (0 þ 1)-dimensional quantum mechanical models in the large N limit [16], whose lowenergy dynamics is depicted by the Schwarzian action. Whatever gravity dual model we take, the low-energy result is the same and controlled by the Schwarzian action This is why we believe that our calculation is relevant to SYK model. We are not calculating the SYK model, which is about the fermions with random coupling, while we are dealing with the correlation function of bosonic operators without it. IV, we study higher-point correlation functions, the thermal OTOC functions in SK formalism
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