Sachdev–Ye–Kitaev model as Liouville quantum mechanics

  title={Sachdev–Ye–Kitaev model as Liouville quantum mechanics},
  author={Dmitry A. Bagrets and Alexander Altland and Alex Kamenev},
  journal={Nuclear Physics},
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… 

Figures from this paper

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


Remarks on the Sachdev-Ye-Kitaev model
The authors study in detail the quantum mechanical model of $N$ Majorana fermions with random interactions of a few fermions at a time (Sachdev-Ye-Kitaev model) in the large $N$ limit. At low
The spectrum in the Sachdev-Ye-Kitaev model
A bstractThe SYK model consists of N ≫ 1 fermions in 0 + 1 dimensions with a random, all-to-all quartic interaction. Recently, Kitaev has found that the SYK model is maximally chaotic and has
Delocalization transition via supersymmetry in one dimension
We use supersymmetric (SUSY) methods to study the delocalization transition at zero energy in a one-dimensional tight-binding model of spinless fermions with particle-hole symmetric disorder. Like
Liouville Theory as a Model for Prelocalized States in Disordered Conductors.
It is concluded that the renormalization group trajectory of the latter theory lies in the vicinity of the line of critical points of the Liouville model.
Effective theory for midgap states in doped spin-ladder and spin-Peierls systems: Liouville quantum mechanics
In gapped spin ladder and spin-Peierls systems the introduction of disorder, for example by doping, leads to the appearance of low energy midgap states. The fact that these strongly correlated
Electron-electron interactions in disordered metals: keldysh formalism
We develop a field theory formalism for the disordered interacting electron liquid in the dynamical Keldysh formulation. This formalism is an alternative to the previously used replica technique. In
Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space
We study a two dimensional dilaton gravity system, recently examined by Almheiri and Polchinski, which describes near extremal black holes, or more generally, nearly $AdS_2$ spacetimes. The
Structure Constants and Conformal Bootstrap in Liouville Field Theory
An analytic expression is proposed for the three-point function of the exponential fields in the Liouville field theory on a sphere. In the classical limit it coincides with what the classical
Liouville theory revisited
We try to develop a coherent picture of Liouville theory as a two-dimensional conformal field theory that takes into account the perspectives of the path-integral approach, bootstrap, canonical
Bekenstein-Hawking Entropy and Strange Metals
We examine models of fermions with infinite-range interactions which realize non-Fermi liquids with a continuously variable U(1) charge density $\mathcal{Q}$, and a non-zero entropy density