Large-N SYK Models

Abstract

Recently, the investigation into the Sachdev-Ye-Kitaev (SYK) model and its variations reemerged in the literature, motivated both by its likely connection with the two-dimensional quantum gravity and by its possible application to describing gapless many-body systems. While a spontaneous symmetry breaking has been discovered in the two coupled SYK model [1], it is unclear whether similar phenomenon could exist in the generalized SYK models with Yukawa-type interactions. In this thesis, we first look deeper into the two coupled SYK model, using a high-efficiency exact diagonalization (ED) tool to study its symmetry-breaking spectrum. Besides giving further verification of and illustration for the physical picture described in [1], our numerical tool also allows us to compute the overlap between the model’s ground state and the thermofield double (TFD) states. In the remaining part of this thesis, we propose a generalized SYK model with Yukawa interactions, focusing on the charge conjugation symmetry (C symmetry) of this model. While tentative numerical results suggest a spontaneous breaking of this symmetry, we have not found a clear prediction for such instability from the model’s bilinear spectrum, either assuming or discarding the C symmetry. We point to limitations of our work and suggest directions for future studies.