TY - JOUR

T1 - Zn modified XY and Goldstone models and vortex confinement transition

AU - Kobayashi, Michikazu

AU - Nitta, Muneto

N1 - Funding Information:
We thank Chandrasekhar Chatterjee for a discussion at the early stage of this work and him and Gergely Fejős for collaboration of the previous paper. This work was supported by the Ministry of Education, Culture, Sports, Science (MEXT)-Supported Program for the Strategic Research Foundation at Private Universities “Topological Science” (Grant No. S1511006) and JSPS KAKENHI Grant No. 16H03984 (M. K. and M. N.). This work is also supported in part by JSPS KAKENHI Grant No. 18H01217 (M. N.). The work of M. N. is also supported in part by a Grant-in-Aid for Scientific Research on Innovative Areas “Topological Materials Science” (KAKENHI Grant No. 15H05855) from MEXT of Japan.
Publisher Copyright:
© 2020 authors.

PY - 2020/4/15

Y1 - 2020/4/15

N2 - 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 Zn 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 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 C/Zn orbifold geometry.

AB - 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 Zn 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 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 C/Zn orbifold geometry.

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U2 - 10.1103/PhysRevD.101.085003

DO - 10.1103/PhysRevD.101.085003

M3 - Article

AN - SCOPUS:85084668173

SN - 2470-0010

VL - 101

JO - Physical Review D

JF - Physical Review D

IS - 8

M1 - 085003

ER -