Collisionless dynamics of general non-Fermi liquids from hydrodynamics of emergent conserved quantities

TL;DR

This paper demonstrates that the hydrodynamics of emergent conserved quantities in non-Fermi liquids leads to collisionless dynamics identical to Fermi liquids in the low-temperature regime, revealing universal behavior in strongly coupled metals.

Contribution

It shows that an infinite-dimensional emergent symmetry group in metals implies collisionless Boltzmann dynamics, extending Fermi liquid behavior to a broader class of non-Fermi liquids.

Findings

Hydrodynamics of emergent conserved quantities reproduces Fermi liquid dynamics.

Collisionless regime predictions are universal for spinless metals.

Differences observed in spinful metals suggest limitations to universality.

Abstract

Given the considerable theoretical challenges in understanding strongly coupled metals and non-Fermi liquids, it is valuable to have a framework to understand properties of metals that are universal, in the sense that they must hold in any metal. It has previously been argued that an infinite-dimensional emergent symmetry group is such a property, at least for clean, compressible metals. In this paper, we will show that such an emergent symmetry group has very strong implications for the dynamics of the metal. Specifically, we show that consideration of the hydrodynamics of the associated infinitely many emergent conserved quantities automatically recovers the collisionless Boltzmann equation that governs the dynamics of a Fermi liquid. Therefore, the hydrodynamic prediction is that in the low-temperature, collisionless regime where the emergent conservation laws hold, the dynamics and response to external fields of a general spinless metal will be identical to a Fermi liquid. We discuss some potential limitations to this general statement, including the possibility of non-hydrodynamic modes. We also report some interesting differences in the case of spinful metals.