Year: 2020
Type: article
Abstract: The modified XY model is a modification of the XY model by the 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 metastable 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 that, for the case of $n=3$, a rod-shaped molecule is the most stable, while a $\mathsf{Y}$-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.
Authors: Michikazu Kobayashi, Muneto Nitta
Institutions: Kyoto University, Keio University
Language: Latvian
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Awards: G1021175238, Symmetry and Topology in Field Theory and Condensed Matter Theory, Search for novel non-equilibrium phase transitions dominated by topological defects, G5168649240, G5544472467, Study of stochastic partial differential equations arising in quantum fluid dynamics, G7304722327, G7312432397, Nonperturbative formulation of quantum field theories based on resurgence theory
OpenAlex ID: W2995643625