# Competition between Chaotic and Non-Chaotic Phases in a Quadratically Coupled Sachdev-Ye-Kitaev Model

## TL;DR

This paper explores a generalized SYK model with two coupled Majorana mode sets, revealing a quantum phase transition between two non-Fermi liquid chaotic phases and characterizing the phase diagram through spectral, Lyapunov, and entropy measures.

## Contribution

It introduces a solvable generalized SYK model with quadratic coupling, demonstrating a quantum phase transition between distinct non-Fermi liquid phases and analyzing finite temperature effects.

## Key findings

- Identifies a zero-temperature quantum phase transition driven by mode ratio.
- Characterizes phase diagram via spectral function, Lyapunov exponent, and entropy.
- Discovers a finite-temperature non-Fermi liquid phase emerging at criticality.

## Abstract

The Sachdev-Ye-Kitaev (SYK) model is a concrete solvable model to study non-Fermi liquid properties, holographic duality and maximally chaotic behavior. In this work, we consider a generalization of the SYK model that contains two SYK models with different number of Majorana modes coupled by quadratic terms. This model is also solvable, and the solution shows a zero-temperature quantum phase transition between two non-Fermi liquid chaotic phases. This phase transition is driven by tuning the ratio of two mode numbers, and a Fermi liquid non-chaotic phase sits at the critical point with equal mode number. At finite temperature, the Fermi liquid phase expands to a finite regime. More intriguingly, a different non-Fermi liquid phase emerges at finite temperature. We characterize the phase diagram in term of the spectral function, the Lyapunov exponent and the entropy. Our results illustrate a concrete example of quantum phase transition and critical regime between two non-Fermi liquid phases.