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arXiv · 1912.09456

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

Michikazu Kobayashi·Muneto Nitta
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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.

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Michikazu Kobayashi, Muneto Nitta. 2019-12-19. $\mathbb{Z}_n$ modified XY and Goldstone models and vortex confinement transition. https://doi.org/10.1103/physrevd.101.085003

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