Lattice gauge theory for condensed matter physics: ferromagnetic superconductivity as its example

Abstract

Recent theoretical studies of various strongly-correlated systems in condensed matter physics reveal that the lattice gauge theory (LGT) developed in high-energy 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 Ginzburg-Landau 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.

Atomic quantum simulation of a three-dimensional U(1) gauge-Higgs model

“…We take the gauge-invariant expressionZ GH of Eq. (19) and update both the gauge field θ x,µ and the Higgs field ϕ x . This process is known to accelerate the convergence of the Markov process more than using the gauge-fixed expression Z GH of Eq.…”

“…By replacing Φ x as Φ x → γ/ √ 2∆τ × φ x and choosing as ρ ′ 0 γ 2 /(2∆τ ) = ρ 0 , we obtainZ GH of Eq. (19). This implies thatZ GH restricts the physical states in the hard-constraint level of Eq.…”

“…Since then, various models of LGT have been studied, both analytically and numerically, in various fields of physics, including high energy physics [18], condensed matter physics [19,20], neural networks [21], etc.…”

“…LGT was introduced by Wilson in 1974 [17] to study the mechanism of quark confinement in strong interactions. Since then, various models of LGT have been studied, both analytically and numerically, in various fields of physics, including high energy physics [18], condensed matter physics [19,20], neural networks [21], etc.…”

“…Second, we list and stress the importance of quantum simulation of nonrelativistic models of LGT themselves in condensed matter physics. In this field, the gauge-theoretical approach has proved to be a powerful method to understand and describe physical phenomena [19], especially for systems with strong correlations [20]. The explicit results for the time development of an electric flux obtained in Sec.…”