All-order fluctuating hydrodynamics of the SYK lattice

TL;DR

This paper derives a fluctuating hydrodynamics framework for the SYK lattice, connecting microscopic quantum chaos models to macroscopic transport phenomena.

Contribution

It develops an effective field theory for hydrodynamics from the SYK lattice's microscopic description, including high-order transport coefficients.

Findings

Hydrodynamic effective action computed to high derivative orders

All transport coefficients explicitly determined

Hydrodynamics embedded into the microscopic SYK lattice model

Abstract

The SYK model has played an important role in recent developments in many-body quantum chaos. We study a spatially local generalisation of it: the SYK lattice. Starting from the nonlinear action of pseudo-Goldstone bosons that dominate its dynamics at low temperatures, in the long wavelength limit we reorganise this action as the effective field theory for fluctuating hydrodynamics, thereby showing how the hydrodynamic degrees of freedom embed into the microscopic description of the model. We compute the hydrodynamic effective action to high orders in the derivative expansion and determine all the corresponding transport coefficients. Hence this work derives hydrodynamics from the microscopic description of a strongly coupled quantum many-body system.