Heat Bath Approach to Landau Damping and Pomeranchuk Quantum Critical Points

TL;DR

This paper introduces a novel approach inspired by heat bath methods to analyze Landau damping near Pomeranchuk quantum critical points, providing insights into quantum phase transitions and dynamical exponents in Fermi liquids.

Contribution

It reformulates the Landau damping problem using a heat bath analogy, deriving results consistent with Fermi liquid theory and applying them to electronic nematic instabilities.

Findings

Landau damping derived via a heat bath approach

Reproduction of known Fermi liquid results

Identification of dynamical exponent z=3 for nematic instability

Abstract

We study the problem of the damping of collective modes close to a Pomeranchuk quantum critical point in a Fermi liquid. In analogy with problems in dissipative open quantum systems, we derive the Landau damping of a Fermi liquid by integrating out a macroscopic number of degrees of freedom from a generating functional. Being a reformulation of the linearized Boltzmann equation this approach reproduces well-known results from the theory of Fermi liquids. We also study the Bethe-Salpeter equations within the Landau theory and discuss the implications of these results on quantum phase transitions of the Pomeranchuk type and its dynamical exponent, z. We apply our results to the electronic nematic instability and find z=3 in the collisionless limit.