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kosterlitz–thouless phase transition

Cambridge University Press (1)

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22 - Field Theory Solitons for Condensed Matter: The XY and Rotor Model, Spins, Superconductivity, and the KT Transition
from Part II - Solitons and Topology; Non-Abelian Theory
Horaƫiu Năstase, Universidade Estadual Paulista, São Paulo
Book:

Classical Field Theory

Published online:

04 March 2019

Print publication:

14 March 2019, pp 203-208
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Summary

We consider field theory solitons relevant for condensed matter. We start with a field theory arising from a two-dimensional system of spins, the XY model, leading to the “rotor model,” or “O(2) model”. From the bosonic Hubbard model, we show a representation that leads to the same quantum rotor model. In the continuum limit, we obtain a massless scalar that has a global vortex as its solution. The dynamics of these vortices is relevant for the Kosterlitz–Thouless (KT) phase transition, a quantum phase transition appearing for instance in 2+1 dimensional superconductivity. The bosonic Hubbard model leads, in the continuum limit, also to a relativistic Landau–Ginzburg model, that has a kink-like solution.