XY model on the circle: diagonalization, spectrum, and forerunners of the quantum phase transition

Details XY model on the circle: diagonalization, spectrum, and forerunners of the quantum phase transition XY model on the circle: diagonalization, spectrum, and forerunners of the quantum phase transition

2008-08-11

arxiv.org/abs/0808.1478v1

Phys. Rev. A 80, 032102 (2009)

Physics

Quantum Physics

29 pages, 16 figures

Scientific paper

10.1103/PhysRevA.80.032102

We exactly diagonalize the finite-size XY model with periodic boundary conditions and analytically determine the ground state energy. We show that there are two types of fermions: singles and pairs, whose dispersion relations have a completely arbitrary gauge-dependent sign. It follows that the ground state is determined by a competition between the vacuum states (with a suitable gauge) of two parity sectors. We finally exhibit some points in finite size systems that forerun criticality. They are associated to single Bogoliubov fermions and to the level crossings between physical and unphysical states. In the thermodynamic limit they approach the ground state and build up singularities at logarithmic rates.

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