Notes on the complex Sachdev-Ye-Kitaev model

We describe numerous properties of the Sachdev-Ye-Kitaev model for complex fermions withN$\gg$ 1 flavors and a global U(1) charge. We provide a general definition of the charge in the (G,Σ) formalism, and compute its universal relation to the infrared asymmetry of the Green function. The same relation is obtained by a renormalization theory. The conserved charge contributes a compact scalar field to the effective action, from which we derive the many-body density of states and extract the charge compressibility. We compute the latter via three distinct numerical methods and obtain consistent results. Finally, we present a two dimensional bulk picture with free Dirac fermions for the zero temperature entropy.

• NS
  National Science Foundation
• UD
  U.S. Department of Energy
• GA
  Gordon and Betty Moore Foundation

  Award: GBMF-4306