Sign-problem-free variant of the complex Sachdev-Ye-Kitaev model

We construct a sign-problem-free variant of the complex Sachdev-Ye-Kitaev (SYK) model which keeps all the essential properties of the SYK model, including the analytic solvability in the large-N limit and being maximally chaotic. In addition to the number of complex fermions N, our model has an additional parameter M controlling the number of terms in the Hamiltonian which we take M -> infinity with keeping M/N constant in the large-N limit. While our model respects global U(1) symmetry associated with the fermion number conservation, both the large-N limit and the sign-problem-free nature become explicit in the Majorana representation. We present a detailed analysis on our model, i.e., the random matrix classification based on the symmetry analysis, analytic approach, and the quantum Monte Carlo simulations. All these analyses show that our model exhibits a non-Fermi-liquid physics, a gapless fermionic system lying beyond the conventional Fermi-liquid picture.