${\mathbb{Z}}_n$ modified XY and Goldstone models and vortex confinement transition

Abstract

The modified XY model is a modification of the XY model by addition of a half-periodic term. The modified Goldstone model is a regular and continuum version of the modified XY model. The former admits a vortex molecule, that is, two half-quantized vortices connected by a domain wall, as a regular topological soliton solution to the equation of motion while the latter admits it as a singular configuration. Here we define the ${\mathbb{Z}}_n$ modified XY and Goldstone models as the $n=2$ case to be the modified XY and Goldstone models, respectively. We exhaust all stable and metastalble vortex solutions for $n=2,3$ and find a vortex confinement transition from an integer vortex to a vortex molecule of $n$ $1/n$-quantized vortices, depending on the ratio between the term of the XY model and the modified term. We find for the case of $n=3$, a rod-shaped molecule is the most stable while a Y-shaped molecule is metastable. We also construct some solutions for the case of $n=4$.The vortex confinement transition can be understood in terms of the $\mathbb{C}/{\mathbb{Z}}_n$ orbifold geometry.

11 pages, 4 figures

References in corpus (13)

• Superfluidity and phase transitions in a resonant Bose gas
• Confinement of Half-quantized Vortices in Coherently Coupled Bose-Einstein Condensates: Simulating Quark Confinement in QCD
• Berezinskii-Kosterlitz-Thouless transition of two-component Bose mixtures with inter-component Josephson coupling
• Competing nematic interactions in a generalized XY model in two and three dimensions
• Size and dynamics of vortex dipoles in dilute Bose-Einstein condensates
• Vortex dynamics in coherently coupled Bose-Einstein condensates
• Correlation length in a generalized two-dimensional XY model
• Deconfinement transitions in a generalised XY model
• $XY$ model with higher-order exchange
• Berezinskii-Kosterlitz-Thouless transition of spin-1 spinor Bose gases in the presence of the quadratic Zeeman effect
• Magnetic quasi-long-range ordering in nematics due to competition between higher-order couplings
• Mesoscopics of half-quantum vortex pair deconfinement in a trapped spin-one condensate
• Vortex confinement transitions in the modified Goldstone model

Cited by in corpus (4)

• Emergent Potts Order in a Coupled Hexatic-Nematic XY model
• Fractional Skyrmion molecules in a $\mathbb{C}{P}^{N-1}$ model
• Topological confinement of vortices in two-flavor dense QCD
• Ordering kinetics and steady states of XY-model with ferromagnetic and nematic interaction