Symmetry and causality constraints on Fermi liquids

TL;DR

This paper explores how symmetry and causality principles impose constraints on the parameters and responses of Fermi liquids, including scale invariance and conformal symmetry, with implications for their microscopic models.

Contribution

It reveals new constraints on Fermi liquid parameters derived from symmetry and causality, especially for conformal Fermi liquids, and examines their effects on nonlinear response.

Findings

Scale invariance constrains the Landau parameter F_0.

Causality restricts the particle-hole continuum and zero sound.

Generalized Landau parameters are affected by symmetry constraints.

Abstract

We investigate symmetry and causality constraints on interacting Fermi liquids. Whereas Galilean or Lorentz boost symmetry leads to a well-known constraint on the first Landau parameter $F_1$, we show that scale invariance similarly constrains $F_0$. In the case of conformal Fermi liquids, we show that causality constraints on the particle-hole continuum and on zero sound strongly restrict the available parameter space for interacting Fermi liquids. We also consider nonlinear response, which we show is sensitive to additional ``generalized Landau parameters'' even at lowest orders in the long wavelength limit. We impose Galilean, Lorentz and scale symmetry on these generalized Landau parameters, obtaining further nonlinear constraints. We test our constraints in several microscopic models that enter a Fermi liquid phase.