Kakutani Dichotomy on Free States

Two quasi-free states on a CAR or CCR algebra are shown to generate quasi-equivalent representations unless they are disjoint.Comment: 12 page

CP^1+U(1) Lattice Gauge Theory in Three Dimensions: Phase Structure, Spins, Gauge Bosons, and Instantons

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 gauge-boson 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 {\it 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 $N$.Comment: Discussion of finite size scaling, O(4) spin correlation adde

Heavy Quark Interactions in Finite Temperature QCD

We study the free energy of a heavy quark-antiquark pair in a thermal medium. We constuct a simple ansatz for the free energy for two quark flavors motivated by the Debye-H\"uckel theory of screening.Comment: 4 pages, 4 figures, contribution to the proceedings of the International Conference on Hard and Electromagnetic Probes of High Energy Nuclear Collisions, Ericeira, Portugal, Nov. 4-10, 200