2008/08/11 by Antonella De Pasquale, A. De Pasquale, Paolo Facchi +1
Mathematics · Physics and Astronomy · #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Quantum many-body systems #cond-mat.stat-mech #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1103/physreva.80.032102
published as Phys. Rev. A 80, 032102 (2009) · 29 pages, 16 figures
arxiv created 2008/08/11 · openalex publication_date 2009/09/03 · arxiv updated 2012/05/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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 Bogoliubov fermions, singles and pairs, whose dispersion relations have a completely arbitrary gauge-dependent sign. It follows that the ground state can be 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.