Cure to the Landau-Pomeranchuk and Associated Long-Wavelength Fermi-surface Instabilities on Lattices

TL;DR

This paper demonstrates that anisotropic gapped states can resolve Landau-Pomeranchuk instabilities in fermionic systems, providing criteria for long-wavelength instabilities on lattices that could help identify hidden order parameters in metals.

Contribution

It introduces a general framework for curing Landau-Pomeranchuk instabilities in lattice fermions using anisotropic gaps and derives criteria based on self-energy derivatives.

Findings

Anisotropic gaps can eliminate L-P instabilities.

Criteria for instabilities involve derivatives of self-energy.

Results applicable to hidden order in metals.

Abstract

The cure to the $\ell=1$ Landau-Pomeranchuk (L-P) instabilities in translationally invariant fermions is shown to be a state with an anisotropic gap at the fermi-surface. For higher $\ell$ and for fermions on a lattice, general criteria for long wavelength instabilities and their cure are found in terms of the derivatives of the single particle self-energy with respect to momentum for spin-symmetric instabilities and with respect to magnetic field for spin-antisymmetric instabilities. The results may be relevant to identifying hidden order parameters found in many metals.