Quasiparticle tunnelling in two coupled chiral SYK model

TL;DR

This paper investigates coupled chiral SYK models in 1+1 dimensions, revealing gapless collective modes and quasiparticle tunnelling without mass gap formation, contrasting with zero-dimensional SYK models.

Contribution

It provides an analytic perturbative solution for coupled chiral SYK models, showing the persistence of gapless modes and unchanged entropy despite interactions.

Findings

No mass gap develops in the coupled 1+1D chiral SYK system.

Massless collective bosonic modes emerge at zero temperature.

Thermodynamic entropy remains unchanged by weak coupling.

Abstract

The chiral SYK model is an 1+1 dimensional generalisation of the Sachdev-Ye-Kitaev model with chiral Majorana fermions and homogeneous random interactions. In the large N limit, the model admits an exact solution of the two-point function due to its scaling symmetry and exhibits a quantised thermal Hall conductance consistent with that of a 2+1 dimensional gapped topological system. We study two chiral SYK systems coupled by a relevant quadratic interaction that explicitly breaks scaling and time reversal symmetry. Working in the regime of weak intersystem coupling, we solve the Dyson-Schwinger equations perturbatively and obtain analytic expressions for two-point functions at finite temperature. Unlike the coupled SYK model in 0+1 dimensions, the 1+1 dimensional chiral system does not develop a mass gap, and no thermal phase transition is observed. We show that the leading correction to the thermodynamic free energy is temperature-independent, implying that the entropy density remains identical to that of two uncoupled chiral SYK systems. A real-time analysis of the retarded correlator reveals the emergence of massless collective bosonic modes propagating between the two subsystems at zero temperature, signalling quasiparticle tunnelling without gap generation. Our results demonstrate a sharp qualitative distinction between relevant deformations of SYK models in zero and one spatial dimensions, and highlight the robustness of gapless chiral edge dynamics against explicit scaling symmetry-breaking interactions.