# Sachdev–Ye–Kitaev model as Liouville quantum mechanics

@article{Bagrets2016SachdevYeKitaevMA, title={Sachdev–Ye–Kitaev model as Liouville quantum mechanics}, author={Dmitry A. Bagrets and Alexander Altland and Alex Kamenev}, journal={Nuclear Physics}, year={2016}, volume={911}, pages={191-205} }

Abstract We show that the proper inclusion of soft reparameterization modes in the Sachdev–Ye–Kitaev model of N randomly interacting Majorana fermions reduces its long-time behavior to that of Liouville quantum mechanics. As a result, all zero temperature correlation functions decay with the universal exponent ∝ τ − 3 / 2 for times larger than the inverse single particle level spacing τ ≫ N ln N . In the particular case of the single particle Green function this behavior is manifestation of…

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## 196 Citations

A Note on Sachdev-Ye-Kitaev Like Model without Random Coupling

- Physics
- 2016

We study a description of the large N limit of the Sachdev-Ye-Kitaev (SYK) model in terms of quantum mechanics without quenched disorder. Instead of random couplings, we introduce massive scalar…

Disorder in the Sachdev–Ye–Kitaev model

- Physics
- 2017

Abstract We give qualitative arguments in support of the mesoscopic nature of the Sachdev–Ye–Kitaev (SYK) model in the regime with q 2 / N ≪ 1 with N Majorana particles coupled by antisymmetric and…

Notes on the complex Sachdev-Ye-Kitaev model

- Physics
- 2020

We describe numerous properties of the Sachdev-Ye-Kitaev model for complex fermions with N ≫ 1 flavors and a global U(1) charge. We provide a general definition of the charge in the ( G, Σ)…

Sachdev-Ye-Kitaev Model with Quadratic Perturbations: The Route to a Non-Fermi Liquid.

- Medicine, PhysicsPhysical review letters
- 2018

Stability of the Sachdev-Ye-Kitaev (SYK_{4}) model with a large but finite number of fermions N with respect to a perturbation, quadratic in fermionic operators is studied and analytic perturbance theory in the amplitude of the SYK_{2} perturbations is developed.

Non-local reparametrization action in coupled Sachdev-Ye-Kitaev models

- PhysicsJournal of High Energy Physics
- 2021

Abstract
We continue the investigation of coupled Sachdev-Ye-Kitaev (SYK) models without Schwarzian action dominance. Like the original SYK, at large N and low energies these models have an…

Conformality of
1/N
corrections in Sachdev-Ye-Kitaev-like models

- Physics
- 2019

The Sachdev-Ye-Kitaev (SYK) model is a quantum-mechanical model of N Majorana fermions which displays a number of appealing features—solvability in the strong coupling regime, near-conformal…

Decoherence and microscopic diffusion at the Sachdev-Ye-Kitaev model

- PhysicsPhysical Review D
- 2018

Sachdev-Ye-Kitaev (SYK) or embedded random ensembles are models ofN fermions with random k-body interactions. They play an important role in understanding black hole dynamics, quantum chaos, and…

Power-law out of time order correlation functions in the SYK model

- Physics
- 2017

We evaluate the finite temperature partition sum and correlation functions of the Sachdev–Ye–Kitaev (SYK) model. Starting from a recently proposed mapping of the SYK model onto Liouville quantum…

Chaos in a classical limit of the Sachdev-Ye-Kitaev model

- PhysicsPhysical Review B
- 2019

We study chaos in a classical limit of the Sachdev-Ye-Kitaev (SYK) model obtained in a suitably defined large-S limit. The low-temperature Lyapunov exponent is found to depend linearly on…

Chaotic-Integrable Transition in the Sachdev-Ye-Kitaev Model.

- Physics, MedicinePhysical review letters
- 2018

Analytically and numerically it is shown that a generalized SYK model with an additional one-body infinite-range random interaction is still quantum chaotic and retains most of its holographic features for a fixed value of the perturbation and sufficiently high temperature.

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