Vortex confinement transitions in the modified Goldstone model

Chatterjee, Chandrasekhar and Fejős, Gergely and Kobayashi, Michikazu and Nitta, Muneto (2020) Vortex confinement transitions in the modified Goldstone model. Physical Review Research. ISSN 2643-1564

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Abstract

The modified $XY$ model is a variation of the $XY$ model extended by a half periodic term, exhibiting a rich phase structure. As the Goldstone model, also known as the linear O(2) model, can be obtained as a continuum and regular model for the $XY$ model, we define the modified Goldstone model as that of the modified $XY$ model. We construct a vortex, a soliton (domain wall), and a molecule of two half-quantized vortices connected by a soliton as regular solutions of this model. Then we investigate its phase structure in two Euclidean dimensions via the functional renormalization group formalism and full numerical simulations. We argue that the field dependence of the wave function renormalization factor plays a crucial role in the existence of the line of fixed points describing the Berezinskii-Kosterlitz-Thouless (BKT) transition, which can ultimately terminate not only at one but at two end points in the modified model. This structure confirms that a two-step phase transition of the BKT and Ising types can occur in the system. We compare our renormalization group results with full numerical simulations, which also reveal that the phase transitions show a richer scenario than expected.

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