How transverse thermal fluctuations disorder a condensate of chiral spirals into a quantum spin liquid

TL;DR

This paper investigates how transverse thermal fluctuations disrupt chiral spiral condensates, leading to a disordered quantum spin liquid state, with implications for four-fermion models and QCD phase diagrams.

Contribution

It demonstrates that transverse fluctuations cause disordering of chiral spiral condensates through double poles in propagators, proposing a universal mechanism for all N > 2.

Findings

Double poles lead to infrared divergences in static modes.

Disorder results in exponential decay with oscillations in two-point functions.

Large N analysis supports the universality of the phenomenon.

Abstract

For a scalar theory with a global $O(N)$ symmetry, when $N=2$ a spatially inhomogeneous condensate arises when the term in the Lagrangian with two spatial derivatives has a negative coefficient. If the condensate for such a chiral spiral includes only one mode, characterized by a momentum $k_0 \hat{z}$, then in perturbation theory at nonzero temperature the propagator for the static mode has a double pole when $\vec{k}^2 = k_0^2$. We conjecture that since chiral spirals spontaneously break both global and spacetime symmetries, that such double poles are a universal property of their static transverse modes. Fluctuations from double poles generate linear infrared divergences in any number of spatial dimensions and disorder the condensate of chiral spirals, analogous to a type of quantum spin liquid. The characteristic feature of this region is that over large spatial distances the two point function is the usual exponential times an oscillatory function. We prove this at large $N$ and suggest this occurs for all $N > 2$. Implications for four-fermion models and the phase diagram of QCD are discussed.