Phase structures of strong coupling lattice QCD with finite baryon and isospin density

Quantum chromodynamics (QCD) at finite temperature (T), baryon chemical potential (\muB) and isospin chemical potential (\muI) is studied in the strong coupling limit on a lattice with staggered fermions. With the use of large dimensional expansion and the mean field approximation, we derive an effective action written in terms of the chiral condensate and pion condensate as a function of T, \muB and \muI. The phase structure in the space of T and \muB is elucidated, and simple analytical formulas for the critical line of the chiral phase transition and the tricritical point are derived. The effects of a finite quark mass (m) and finite \muI on the phase diagram are discussed. We also investigate the phase structure in the space of T, \muI and m, and clarify the correspondence between color SU(3) QCD with finite isospin density and color SU(2) QCD with finite baryon density. Comparisons of our results with those from recent Monte Carlo lattice simulations on finite density QCD are given.Comment: 18 pages, 6 figures, revtex4; some discussions are clarified, version to appear in Phys. Rev.

Finite-Density Massless Two-Color QCD at Isospin Roberge-Weiss Point and 't Hooft Anomaly

We study the phase diagram of two-flavor massless two-color QCD (QC$_2$D) under the presence of quark chemical potentials and imaginary isospin chemical potentials. At the special point of the imaginary isospin chemical potential, called the isospin Roberge--Weiss (RW) point, two-flavor QC$_2$D enjoys the $\mathbb{Z}_2$ center symmetry that acts on both quark flavors and the Polyakov loop. We find a $\mathbb{Z}_2$ 't Hooft anomaly of this system, which involves the $\mathbb{Z}_2$ center symmetry, the baryon-number symmetry, and the isospin chiral symmetry. Anomaly matching, therefore, constrains the possible phase diagram at any temperatures and quark chemical potentials at the isospin RW point, and we compare it with previous results obtained by chiral effective field theory and lattice simulations. We also point out an interesting similarity of two-flavor massless QC$_2$D with $(2+1)$d quantum anti-ferromagnetic systems.Comment: 23 pages, 2 figures, 2 appendices. v2: references are update

Color Superconductivity

We discuss recent results on color superconductivity in QCD at large chemical potential.Comment: to appear in the Proceedings of the 10th International Conference on Recent Progress in Many-Body Theories (MBX), Seattle, WA, 10-15 Sep 1999, R. F. Bishop et al. (eds.), World Scientific (Singapore

Phase diagram of two-color quark matter at nonzero baryon and isospin density

We investigate the properties of cold dense quark matter composed of two colors and two flavors of light quarks. In particular, we perform the first model calculation of the full phase diagram at nonzero baryon and isospin density, thus matching the model-independent predictions of chiral perturbation theory at low density to the conjectured phase structure at high density. We confirm the presence of the Fulde-Ferrell (FF) phase in the phase diagram and study its dependence on the tunable parameter in the Lagrangian that simulates the effects of the quantum axial anomaly. As a byproduct, we clarify the calculation of the thermodynamic potential in the presence of the FF pairing, which was previously based on an ad hoc subtraction of an unphysical cutoff artifact. Furthermore, we argue that close to the diquark (or pion) Bose-Einstein condensation transition, the system behaves as a dilute Bose gas so that our simple fermionic model in the mean-field approximation is not quantitatively adequate. We suggest that including thermal fluctuations of the order parameter for Bose-Einstein condensation is crucial for understanding available lattice data.Comment: 14 pages, REVTeX4-1, 7 eps figures; v2: minor modifications + references added; version to be published in Phys. Rev.