Lattice AbelianHiggs model with noncompact gauge fields
Abstract
We consider a noncompact lattice formulation of the threedimensional electrodynamics with N component complex scalar fields, i.e., the lattice AbelianHiggs model with noncompact gauge fields. For any N ≥2 , the phase diagram shows three phases differing for the behavior of the scalarfield and gaugefield correlations: The Coulomb phase (shortranged scalar and longranged gauge correlations), the Higgs phase (condensed scalarfield and gapped gauge correlations), and the molecular phase (condensed scalarfield and longranged gauge correlations). They are separated by three transition lines meeting at a multicritical point. Their nature depends on the phases they separate, and on the number N of components of the scalar field. In particular, the Coulombtomolecular transition line (where gauge correlations are irrelevant) is associated with the LandauGinzburgWilson Φ^{4} theory sharing the same SU(N ) global symmetry but without explicit gauge fields. On the other hand, the CoulombtoHiggs transition line (where gauge correlations are relevant) turns out to be described by the continuum AbelianHiggs field theory with explicit gauge fields. Our numerical study is based on finitesize scaling analyses of Monte Carlo simulations with C^{*} boundary conditions (appropriate for lattice systems with noncompact gauge variables, unlike periodic boundary conditions), for several values of N , i.e., N =2 , 4, 10, 15, and 25. The numerical results agree with the renormalizationgroup predictions of the continuum field theories. In particular, the CoulombtoHiggs transitions are continuous for N ≳10 , in agreement with the predictions of the AbelianHiggs field theory.
 Publication:

Physical Review B
 Pub Date:
 February 2021
 DOI:
 10.1103/PhysRevB.103.085104
 arXiv:
 arXiv:2010.06311
 Bibcode:
 2021PhRvB.103h5104B
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Strongly Correlated Electrons;
 High Energy Physics  Lattice
 EPrint:
 19 pages, 24 eps figures