Lattice gauge theory for condensed matter physics: ferromagnetic superconductivity as its example
Abstract
Recent theoretical studies of various stronglycorrelated systems in condensed matter physics reveal that the lattice gauge theory (LGT) developed in highenergy physics is quite a useful tool to understand physics of these systems. Knowledge of LGT is to become a necessary item even for condensed matter physicists. In the first part of this paper, we present a concise review of LGT for the reader who wants to understand its basics for the first time. For illustration, we choose the Abelian Higgs model, a typical and quite useful LGT, which is the lattice version of the GinzburgLandau model interacting with a U(1) gauge field (vector potential). In the second part, we present an account of the recent progress in the study of ferromagnetic superconductivity (SC) as an example of application of LGT to topics in condensed matter physics. As the ferromagnetism (FM) and SC are competing orders with each other, large fluctuations are expected to take place and therefore nonperturbative methods are required for theoretical investigation. After we introduce a LGT describing the FMSC, we study its phase diagram and topological excitations (vortices of Cooper pairs) by Monte Carlo simulations.
 Publication:

Modern Physics Letters B
 Pub Date:
 September 2014
 DOI:
 10.1142/S0217984914300129
 arXiv:
 arXiv:1408.0089
 Bibcode:
 2014MPLB...2830012I
 Keywords:

 Lattice gauge theory;
 stronglycorrelated systems;
 Ginzburg–Landau theory;
 ferromagnetic superconductivity;
 Monte Carlo simulation;
 pathintegral;
 Condensed Matter  Strongly Correlated Electrons;
 High Energy Physics  Lattice
 EPrint:
 31 pages, 13 figures, Invited review article of Mod.Phys.Lett.B