Role of fluctuations for density-wave instabilities: Failure of the mean-field description

TL;DR

This paper investigates how fluctuations affect density-wave instabilities, revealing that mean-field theory fails for certain systems due to significant fluctuation corrections, especially in charge and spin density waves with Heisenberg symmetry.

Contribution

It demonstrates the failure of mean-field descriptions in density-wave systems with real N-component order parameters, highlighting the importance of fluctuation effects beyond mean-field approximations.

Findings

Fluctuation corrections cancel in XY magnets, validating mean-field theory.

In systems with N≠2, fluctuations are significant and invalidate mean-field assumptions.

Logarithmic fluctuation contributions originate from intermediate length-scale quasiparticle interactions.

Abstract

Density-wave instabilities have been observed and studied in a multitude of materials. Most recently, in the context of unconventional superconductors like the iron-based superconductors, they have excited considerable interest. We analyze the fluctuation corrections to the equation of state of the density-wave order parameter for commensurate charge-density waves and spin-density waves due to perfect nesting. For XY magnets, we find that contributions due to longitudinal and transverse fluctuations cancel each other, making the mean-field analysis of the problem controlled. This is consistent with the analysis of fluctuation corrections to the BCS theory of superconductivity [S. Kos, A. J. Millis, and A. I. Larkin, Phys. Rev. B 70, 214531 (2004)]. However, this cancellation does not occur in density-wave systems when the order parameter is a real $N$-component object with $N\neq2$. Then, the number of transverse fluctuating modes differs from the number of longitudinal fluctuating modes. Indeed, in the case of charge-density waves as well as spin-density waves with Heisenberg symmetry, we find that fluctuation corrections are not negligible, and hence mean-field theories are not justified. These singular fluctuations originate from the intermediate length-scale regime, with wavelengths between the lattice constant and the $T=0$ correlation length. The resulting logarithmic fluctuation contributions to the gap equation originate from the derivative of the anomalous polarization function, and the crucial process is an interaction of quasiparticles through the exchange of fluctuations.