Vortices and composite order in $\mathrm{SU}(N)$ theories coupled to Abelian gauge field

TL;DR

This paper studies SU(N) Ginzburg-Landau models coupled to Abelian gauge fields, revealing two phase transitions and a neutral composite order phase for large gauge couplings, with implications for vortex lattice formation.

Contribution

It demonstrates the existence of a novel neutral composite order phase in SU(N) models with N>2 and characterizes the phase structure and vortex behavior at finite temperature.

Findings

Existence of two phase transitions for large gauge couplings.

Identification of a neutral phase with composite order and no Meissner effect.

Vortex lattice formation at low temperatures in external fields.

Abstract

We consider $\mathrm{SU}(N)$-symmetric Ginzburg-Landau models coupled to non-compact Abelian gauge field focusing on the case $N > 2$ at finite temperature. We show that, at least for sufficiently large gauge-field coupling constants, these models have two phase transitions. The intermediate phase between the symmetric and low-temperature phases is a state with composite neutral order and no Meissner effect. In this neutral phase the system spontaneously breaks only the symmetry associated with phase differences and density differences between components. For $N > 2$, in contrast to the $SU(2)$ case, the neutral state cannot be mapped onto an $\mathrm{O}(M)$ model. We term this state ${\mathbb{C}{P}}^{N-1}$-neutral phase. We also show that while $\mathrm{SU}(N)$-symmetric Ginzburg-Landau models are not superconductors or superfluids in the usual sense, their state in external field at sufficiently low temperature is a vortex lattice.