Sign-Problem-Free Variant of Complex Sachdev-Ye-Kitaev Model

TL;DR

This paper introduces a sign-problem free variant of the complex SYK model that retains key properties like solvability and chaos, enabling detailed analysis of non-Fermi liquid physics.

Contribution

The authors develop a new complex SYK model variant that is sign-problem free and maintains essential features, facilitating advanced numerical and analytical studies.

Findings

Model exhibits non-Fermi liquid behavior

Analytic and Monte Carlo methods confirm properties

Model retains maximal chaos and solvability

Abstract

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 $M \to \infty$ 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 analysis show that our model exhibit a non-Fermi liquid (NFL) physics, a gapless fermionic system lying beyond the conventional Fermi liquid picture.