In this paper we study a 3D lattice spin model of CP 1 Schwinger-bosons coupled with dynamical compact U(1) gauge bosons. The model contains two parameters; the gauge coupling and the hopping parameter of CP 1 bosons. At large (weak) gauge couplings, the model reduces to the classical O(3) (O(4)) spin model with long-range and/or multi-spin interactions. It is also closely related to the recently proposed "Ginzburg-Landau" theory for quantum phase transitions of s = 1/2 quantum spin systems on a 2D square lattice at zero temperature. We numerically study the phase structure of the model by calculating specific heat, spin correlations, instanton density, and gaugeboson mass. The model has two phases separated by a critical line of second-order phase transition; O(3) spin-ordered phase and spin-disordered phase. The spin-ordered phase is the Higgs phase of U(1) gauge dynamics, whereas the disordered phase is the confinement phase. We find a crossover in the confinement phase which separates dense and dilute regions of instantons. On the critical line, spin excitations are gapless, but the gauge-boson mass is nonvanishing. This indicates that a confinement phase is realized on the critical line. To confirm this point, we also study the noncompact version of the model. A possible realization of a deconfinement phase on the criticality is discussed for the CP N +U(1) model with larger N .

In this paper, we study the three-dimensional (3D) N f -flavor CP 1 model (a set of N f CP 1 variables) coupled with a dynamical compact U(1) gauge field by means of Monte-Carlo simulations. This model is relevant to 2D s = 1/2 quantum spin models, and has a phase transition line which separates an ordered phase of global spin symmetry from a disordered one. From a gauge theoretical point of view, the ordered phase is a Higgs phase whereas the disordered phase is a confinement phase. We are interested in the gauge dynamics just on the critical line, in particular, whether a Coulomblike deconfinement phase is realized there. This problem is quite important to clarify low-energy excitations in certain class of quantum spin models. If the gauge dynamics is in the deconfinement phase there, spinons, which transform in the fundamental representation of the SU(N f ) symmetry, appear as low-energy excitations. By Monte-Carlo simulations, we found that the "phase structure" on the criticality strongly depends on the value of N f . For small N f , the confinement phase is realized, whereas the deconfinement phase appears for sufficient large N f ≥ 14. This result strongly suggests that compact QED3 is in a deconfinement phase for sufficiently large number of flavors of massless fermions.

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

We study the phase structure of the 3D nonlocal compact U(1) lattice gauge theory coupled with a Higgs field by Monte Carlo simulations. The nonlocal interactions among gauge variables are along the temporal direction and mimic the effect of local coupling to massless particles. In contrast to the 3D local abelian Higgs model having only the confinement phase, the present model exhibits the confinement, Higgs, and Coulomb phases separated by three second-order transition lines emanating from a triple point. This suggests that electron fractionalization phenomena in strongly-correlated electron systems may take place not only in the Coulomb phase but also in the Higgs phase.

In this paper, we study a 3D compact U(1) lattice gauge theory with a variety of nonlocal interactions that simulates the effects of gapless/gapful matter fields. We restrict the nonlocal interactions among gauge variables only to those along the temporal direction and adjust their coupling constants optimally to simulate the isotropic nonlocal couplings of the original model. This theory is quite important to investigate the phase structures of QED 3 and strongly-correlated electron systems like the 2D quantum spin models, the fractional quantum Hall effect, the t-J model of high-temperature superconductivity. We perform numerical studies of this theory to find that, for a certain class of power-decaying couplings, there appears a second-order phase transition to the deconfinement phase as the gauge coupling constant is decreased. On the other hand, for the exponentiallydecaying coupling, there are no signals for second-order phase transition. These results indicate the possibility that introduction of sufficient number of massless matter fields destabilizes the permanent confinement in the 3D compact U(1) pure gauge theory due to instantons.