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 $k_0\hat{z}$, 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.

v2: added a discussion of previous work by Kleinert, ref. 10

References in corpus (19)

• Inhomogeneous chiral condensates
• Inhomogeneous phases in the Nambu-Jona-Lasino and quark-meson model
• Susceptibilities near the QCD (tri)critical point
• Dynamic universality class of the QCD critical point
• Self-consistent crystalline condensate in chiral Gross-Neveu and Bogoliubov-de Gennes systems
• A Twisted Kink Crystal in the Chiral Gross-Neveu model
• Scrutinizing the pion condensed phase
• Inhomogeneous phases in the quark-meson model with vacuum fluctuations
• Covering the Fermi Surface with Patches of Quarkyonic Chiral Spirals
• Inhomogeneous charged pion condensation in chiral asymmetric dense quark matter in the framework of NJL${}_2$ model
• Inhomogeneous chiral condensates in three-flavor quark matter
• Dualities and inhomogeneous phases in dense quark matter with chiral and isospin imbalances in framework of effective model
• Phase structure of the 1+1 dimensional Nambu--Jona-Lasinio model with isospin
• Consistent parameter fixing in the quark-meson model with vacuum fluctuations
• Isotropic Lifshitz critical behavior from the functional renormalization group
• Supersymmetry Breaking in Spatially Modulated Vacua
• Complex Fluids: The Physics of Emulsions
• Chiral Spirals from Noncontinuous Chiral Symmetry: The Gross-Neveu model results
• Quantum Lifshitz criticality in a frustrated two-dimensional XY model

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