Notes on the complex Sachdev-Ye-Kitaev model

Abstract

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) 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.In the infrared (IR), the spectral asymmetry is characterized by the long-time behavior of the Green function G β=∞ (±τ ) ∼ ∓e ±πE τ −2∆ for and τ J −1 , (1.7)or equivalently the small frequency behavior G β=∞ (±iω) ∼ ∓ie ∓iθ ω 2∆−1 for and 0 < ω J , (1.8)

Matrix ensembles with global symmetries and ’t Hooft anomalies from 2d gauge theory

“…1 We also find that the ground state energy in each sector is proportional to the quadratic Casimir c 2 prq. This result is clearly model dependent, but does reproduce the dependence of the ground state energy on the charge in the complex SYK model [35].…”

“…In this appendix, we write down the partition functions on a general Riemann surface for the special case of U p1q symmetry. The motivation for this case is the complex SYK model, see [35] for recent work. Other references include [28,30].…”

“…Another motivation is to explore the effect of 't Hooft anomalies in random matrix theory. Finally, we expect that aspects of this setup (although not the exact connection to random matrix theory) will be relevant for the bulk description of SYK-like theories with global symmetry [28][29][30][31][32][33][34][35].…”

Symmetry classes, many-body zero modes, and supersymmetry in the complex Sachdev-Ye-Kitaev model

“…The key extra structure relevant to us arises if the interaction terms c † i c † j c k c l appear in antisymmetrized combinations of the creation and annihilation operators. This renders the Hamiltonian invariant under c † i ↔ c i and J ij,kl ↔ J * ij,kl [20,35], i.e., we have [H, S] = 0 with the antiunitary chiral symmetry [35,46] S effecting…”

“…The variant of the model with randomly interacting complex fermions shares many properties with the Majorana version, including a nonzero entropy density at zero temperature, but it additionally conserves a U(1) charge [19,20]. The model exhibits compressible states, i.e., the charge density can be tuned by a conjugate chemical potential [19].…”