Perturbed Sachdev-Ye-Kitaev Model: A Polaron in the Hyperbolic Plane

Abstract

We study the Sachdev-Ye-Kitaev (SYK 4 ) model with a weak SYK 2 term of magnitude Γ beyond the simplest perturbative limit considered previously. For intermediate values of the perturbation strength,, fluctuations of the Schwarzian mode are suppressed, and the SYK 4 mean-field solution remains valid beyond the timescale t 0 ∼ N=J up to t à ∼ J=Γ 2 . The out-of-time-order correlation function displays at short time intervals exponential growth with maximal Lyapunov exponent 2πT, but its prefactor scales as T at low temperatures T ≤ Γ.

Non-equilibrium Sachdev-Ye-Kitaev model with quadratic perturbation

“…In the present Letter we extend the approach of Ref. [1] into a broad field of non-equilibrium problems described by Keldysh functional integral methods. We study the simplest physical quantity that may shed some light on the physical significance of the polaron bound-state.…”

“…The Liouville quantum mechanics approach [3,5] to the pure SYK 4 model can be recast into the form of the functional integral over the same Bose field, but in this case bound-states are absent and fluctuations are strong and non-Gaussian. We have shown [1] that quadratic perturbation lead to the formation of the polaron bound-state and thus to suppression of fluctuations at low energies.…”

“…The Sachdev-Ye-Kitaev model [2][3][4][5] modified by random quadratic terms in the Hamiltonian presents a valuable starting point to develop a theory of strongy correlated electron systems. Recent results [1] demonstrate an interesting interplay between soft-mode fluctuations (which dominates the infra-red behavior of the pure SYK 4 model) and SYK 2 terms of moderate magnitude. Namely, it was found that in presence of SYK 2 terms the soft-mode fluctuations become suppressed in a wide temperature range, and can be described by a kind of nearly Gaussian action.…”

“…Namely, it was found that in presence of SYK 2 terms the soft-mode fluctuations become suppressed in a wide temperature range, and can be described by a kind of nearly Gaussian action. The crucial role in this picture is played by the bound-polaron solution obtained in [1] for some collective Bose field. The Liouville quantum mechanics approach [3,5] to the pure SYK 4 model can be recast into the form of the functional integral over the same Bose field, but in this case bound-states are absent and fluctuations are strong and non-Gaussian.…”

Constructing AdS2 flow geometries

“…The microscopic model we analyse is an SYK-type model [16][17][18][19] with two flavours [20] deformed by a relevant deformation. The model is governed by a Hamiltonian of the following form [21][22][23]…”