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

Understand

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.