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Remarks on the Sachdev-Ye-Kitaev model

Juan Maldacena and Douglas Stanford

  • Institute for Advanced Study, Princeton, New Jersey 08540, USA

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Phys. Rev. D 94, 106002 – Published 4 November, 2016

DOI: https://doi.org/10.1103/PhysRevD.94.106002

Abstract

We study a quantum-mechanical model proposed by Sachdev, Ye and Kitaev. The model consists of N Majorana fermions with random interactions of a few fermions at a time. It it tractable in the large-N limit, where the classical variable is a bilocal fermion bilinear. The model becomes strongly interacting at low energies where it develops an emergent conformal symmetry. We study two- and four-point functions of the fundamental fermions. This provides the spectrum of physical excitations for the bilocal field. The emergent conformal symmetry is a reparametrization symmetry, which is spontaneously broken to SL(2,R), leading to zero modes. These zero modes are lifted by a small residual explicit breaking, which produces an enhanced contribution to the four-point function. This contribution displays a maximal Lyapunov exponent in the chaos region (out-of-time-ordered correlator). We expect these features to be universal properties of large-N quantum mechanics systems with emergent reparametrization symmetry. This article is largely based on talks given by Kitaev, which motivated us to work out the details of the ideas described there.

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Phys. Rev. D 94, 106002– Published 4 November, 2016
  • Received 8 September 2016
Article part of CHORUS

© 2016 American Physical Society

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