Notes on the complex Sachdev-Ye-Kitaev model

Abstract

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

v3: typos in appendix A fixed, one reference added; v2: 75 pages, 14 figures, new appendix A.6 and references added; v1: 73 pages, 13 figures, 1 spooky propagator

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