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

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 k0z^, then in perturbation theory at nonzero temperature the propagator for the static mode has a double pole when k2=k02. 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 establish this at large N and suggest that it occurs for all N>2. Implications for fermion models and the phase diagram of QCD at nonzero density are discussed.