Critical theory of Pomeranchuk transitions via high-dimensional bosonization

TL;DR

This paper develops a high-dimensional bosonization approach to derive an effective field theory for Pomeranchuk transitions in 2D Fermi liquids, revealing critical behavior and fixed point structure.

Contribution

It introduces a novel bosonization-based effective field theory for Pomeranchuk transitions, highlighting the critical mode and its dynamical exponent in two dimensions.

Findings

Transition driven by softening eigenmode leading to Fermi surface distortion

Effective theory has dynamical critical exponent z=2

System at upper critical dimension with Gaussian fixed point

Abstract

We use high-dimensional bosonization to derive an effective field theory that describes the Pomeranchuck transition in isotropic two-dimensional Fermi liquids. We find that the transition is triggered by the softening of an eigenmode that leads to spontaneous Fermi surface distortion. The resultant theory in terms of this critical mode has dynamical critical exponent $z = 2$ and the upper critical dimension is $d_c = 4-z= 2$. As a result the system is at the upper critical dimension in 2D, resulting in a Gaussian fixed point with a marginally irrelevant quartic perturbation.