Anisotropic Non-Fermi Liquids

TL;DR

This paper investigates anisotropic non-Fermi liquid states at quantum critical points of SDW and CDW transitions in metals with twofold rotational symmetry, revealing distinct behaviors and emergent properties below three dimensions.

Contribution

It introduces a dimensional regularization approach to analyze non-Fermi liquids at SDW and CDW critical points, highlighting the stable anisotropic non-Fermi liquid at SDW and the breakdown at CDW.

Findings

Stable anisotropic non-Fermi liquid at SDW critical point.

Emergent algebraic nesting near hot spots.

Breakdown of perturbation theory at CDW critical point.

Abstract

We study non-Fermi liquid states that arise at the quantum critical points associated with the spin density wave (SDW) and charge density wave (CDW) transitions in metals with twofold rotational symmetry. We use the dimensional regularization scheme, where a one-dimensional Fermi surface is embedded in $3-\epsilon$ dimensional momentum space. In three dimensions, quasilocal marginal Fermi liquids arise both at the SDW and CDW critical points : the speed of the collective mode along the ordering wavevector is logarithmically renormalized to zero compared to that of Fermi velocity. Below three dimensions, however, the SDW and CDW critical points exhibit drastically different behaviors. At the SDW critical point, a stable anisotropic non-Fermi liquid state is realized for small $\epsilon$, where not only time but also different spatial coordinates develop distinct anomalous dimensions. The non-Fermi liquid exhibits an emergent algebraic nesting as the patches of Fermi surface are deformed into a universal power-law shape near the hot spots. Due to the anisotropic scaling, the energy of incoherent spin fluctuations disperse with different power laws in different momentum directions. At the CDW critical point, on the other hand, the perturbative expansion breaks down immediately below three dimensions as the interaction renormalizes the speed of charge fluctuations to zero within a finite renormalization group scale through a two-loop effect. The difference originates from the fact that the vertex correction anti-screens the coupling at the SDW critical point whereas it screens at the CDW critical point.