Diffusion in higher dimensional SYK model with complex fermions

TL;DR

This paper introduces a higher-dimensional SYK model with complex fermions on bipartite lattices, analyzing its transport properties, diffusion constants, and thermal behavior at low temperatures.

Contribution

It extends the zero-dimensional SYK model to higher dimensions with conserved charge, providing new insights into diffusion and transport in such systems.

Findings

Diffusivity depends on the ratio of free to interacting Majorana fermions.

Thermal conductivity and specific heat are proportional to temperature.

Electrical resistivity exhibits a linear temperature dependence.

Abstract

We construct a new higher dimensional SYK model with complex fermions on bipartite lattices. As an extension of the original zero-dimensional SYK model, we focus on the one-dimension case, and similar Hamiltonian can be obtained in higher dimensions. This model has a conserved U(1) fermion number Q and a conjugate chemical potential \mu. We evaluate the thermal and charge diffusion constants via large q expansion at low temperature limit. The results show that the diffusivity depends on the ratio of free Majorana fermions to Majorana fermions with SYK interactions. The transport properties and the butterfly velocity are accordingly calculated at low temperature. The specific heat and the thermal conductivity are proportional to the temperature. The electrical resistivity also has a linear temperature dependence term.