We introduce a U(1) lattice gauge theory with dual gauge fields and study its phase structure. This system is motivated by unconventional superconductors like extended s-wave and d-wave superconductors in the strongly-correlated electron systems. In this theory, the "Cooper-pair" field is put on links of a cubic lattice due to strong on-site repulsion between electrons in contrast to the ordinary s-wave Cooper-pair field on sites. This Cooper-pair field behaves as a gauge field dual to the electromagnetic U(1) gauge field. By Monte Carlo simulations we study this lattice gauge model and find a first-order phase transition from the normal state to the Higgs (superconducting) state. Each gauge field works as a Higgs field for the other gauge field. This mechanism requires no scalar fields in contrast to the ordinary Higgs mechanism.Introduction. − The Ginzburg-Landau (GL) theory has proved itself a powerful tool to describe the phase transitions of conventional s-wave superconductors. In field-theory terminology, the GL theory takes a form of Abelian Higgs model (AHM), and its phase structure has been studied by field-theoretical techniques and Monte Carlo (MC) simulations of lattice gauge theory. These studies are partly motivated by the work of Halperin, Lubensky, and Ma [1] which predicts a first-order phase transition. At present, it is established that the phase structure of three dimensional (3D) AHM on the lattice strongly depends on a parameter controlling fluctuations of the amplitudes |ϕ(x)| of the Higgs (Cooper-pair) field [2]. At the London limit in which |ϕ(x)| is fixed, there is only the confinement phase in the lattice model. As the fluctuations of |ϕ(x)| are increased, a second-order phase transition to the Higgs phase appears, and for further fluctuations, the transition becomes of first-order.Some strongly-correlated electron systems exhibit unconventional superconductivity (UCSC) [3] at low temperatures (T ). The first d-wave superconductor CeCu 2 Si 2 was discovered in 1979 [4]. In 1986, the cuprate high-T c superconductors were discovered [5], and later, it was found that they are d-wave superconductors. Thus, it is interesting to set up and study the GL theory of the UCSC. In the framework of weak-coupling theory, such studies have appeared [6]. However, the strong-coupling region remains to be studied [7]. In this Letter, we shall introduce a GL theory for the UCSC on a lattice, and study its phase structure by means of MC simulations. We shall see that the order parameter, a bilocal field, is regarded as a gauge field, and the knowledge and method of gauge theory are useful to study this GL lattice gauge theory. We find that this new type of gauge theory has a very interesting phase structure.Lattice gauge model for UCSC. − Let us first consider a UCSC on a 3D spatial lattice. We put a "Cooper-pair

In this paper we shall introduce a lattice model of unconventional superconductors (SC) like d-wave SC in order to study quantum phase transition at vanishing temperature (T ). Finite-T counterpart of the present model was proposed previously with which SC phase transition at finite T was investigated. The present model is a noncompact U(1) lattice-gauge-Higgs model in which the Higgs boson, the Cooper-pair field, is put on lattice links in order to describe d-wave SC. We first derive the model from a microscopic Hamiltonian in the path-integral formalism and then study its phase structure by means of the Monte Carlo simulations. We calculate the specific heat, monopole densities and the magnetic penetration depth (the gauge-boson mass). We verified that the model exhibits a second-order phase transition from normal to SC phases. Behavior of the magnetic penetration depth is compared with that obtained in the previous analytical calculation using XY model in four dimensions. Besides the normal to SC phase transition, we also found that another second-order phase transition takes place within the SC phase in the present model. We discuss physical meaning of that phase transition.

In this paper we shall study quantum critical behavior of lattice model of unconventional superconductors (SC) that was proposed in the previous papers. In this model, the Cooper-pair (CP) field is defined on lattice links in order to describe d-wave SC. The CP field can be regarded as a U (1) lattice gauge field, and the SC phase transition takes place as a result of the phase coherence of the CP field.Effects of the long-range Coulomb interactions between the CP's and fluctuations of the electromagnetic field are taken into account. We investigate the phase structure of the model and the critical behavior by means of the Monte Carlo simulations. We find that the parameter, which controls the fluxes (vortices) of the CP, strongly influences the phase structure. In three-dimensional case, the model has rich phase structure. In particular there is a "monopole proliferation" phase transition besides the SC phase transition. Depending on the parameters, this transition exists within the SC phase or takes place simultaneously with the SC transition. This new type of transition is relevant for unconventional SC's with strong spatial three-dimensionality and to be observed by experiments.

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