Diquark condensation in dense SU(2) matter

We report on a lattice study of two-color QCD with adjoint staggered fermions at high density. We find that the model has no early onset and we report on results for diquark condensation, from simulations with and without a diquark source term.Comment: Lattice2001(hightemp

Lattice Study of Dense Matter with Two Colors and Four Flavors

We present results from a simulation of SU(2) lattice gauge theory with N_f=4 flavors of Wilson fermion and non-zero quark chemical potential mu, using the same 12^3x24 lattice, bare gauge coupling, and pion mass in cut-off units as a previous study with N_f=2. The string tension for N_f=4 is found to be considerably smaller implying smoother gauge field configurations. Thermodynamic observables and order parameters for superfluidity and color deconfinement are studied, and comparisons drawn between the two theories. Results for quark density and pressure as functions of mu are qualitatively similar for N_f=2 and N_f=4; in both cases there is evidence for a phase in which baryonic matter is simultaneously degenerate and confined. Results for the stress-energy tensor, however, suggest that while N_f=2 has a regime where dilute matter is non-relativistic and weakly-interacting, N_f=4 matter is relativistic and strongly-interacting for all values of mu above onset.Comment: Horizontal axes of several figures rescaled. Version accepted for publicatio

The Three Dimensional Thirring Model for N_f=4 and N_f=6

We present Monte Carlo simulation results for the three dimensional Thirring model for numbers of fermion flavors N_f=4 and 6. For N_f=4 we find a second order chiral symmetry breaking transition at strong coupling, corresponding to an ultra-violet fixed point of the renormalisation group defining a non-trivial continuum limit. The critical exponents extracted from a fit to a model equation of state are distinct from those found for N_f=2. For N_f=6, in contrast, we present evidence for tunnelling between chirally symmetric and broken vacua at strong coupling, implying that the phase transition is first order and no continuum limit exists. The implications for the phase diagram of the model in the plane of coupling strength and N_f are briefly discussed.Comment: 29 pages, 13 figure

Application of the Maximum Entropy Method to the (2+1)d Four-Fermion Model

We investigate spectral functions extracted using the Maximum Entropy Method from correlators measured in lattice simulations of the (2+1)-dimensional four-fermion model. This model is particularly interesting because it has both a chirally broken phase with a rich spectrum of mesonic bound states and a symmetric phase where there are only resonances. In the broken phase we study the elementary fermion, pion, sigma and massive pseudoscalar meson; our results confirm the Goldstone nature of the pi and permit an estimate of the meson binding energy. We have, however, seen no signal of sigma -> pi pi decay as the chiral limit is approached. In the symmetric phase we observe a resonance of non-zero width in qualitative agreement with analytic expectations; in addition the ultra-violet behaviour of the spectral functions is consistent with the large non-perturbative anomalous dimension for fermion composite operators expected in this model.Comment: 25 pages, 13 figure

Numerical Study of the Two Color Attoworld

We consider QCD at very low temperatures and non-zero quark chemical potential from lattice Monte Carlo simulations of the two-color theory in a very small spatial volume (the attoscale). In this regime the quark number rises in discrete levels in qualitative agreement with what is found analytically at one loop on S3xS1 with radius R_S3 << 1/{\Lambda}_QCD. The detailed level degeneracy, however, cannot be accounted for using weak coupling arguments. At each rise in the quark number there is a corresponding spike in the Polyakov line, also in agreement with the perturbative results. In addition the quark number susceptibility shows a similar behaviour to the Polyakov line and appears to be a good indicator of a confinement-deconfinement type of transition.Comment: 18 pages, 10 figure

BEC-BCS Crossover in the Nambu--Jona-Lasinio Model of QCD

The BEC-BCS crossover in QCD at finite baryon and isospin chemical potentials is investigated in the Nambu--Jona-Lasinio model. The diquark condensation in two color QCD and the pion condensation in real QCD would undergo a BEC-BCS crossover when the corresponding chemical potential increases. We determined the crossover chemical potential as well as the BEC and BCS regions. The crossover is not triggered by increasing the strength of attractive interaction among quarks but driven by changing the charge density. The chiral symmetry restoration at finite temperature and density plays an important role in the BEC-BCS crossover. For real QCD, strong couplings in diquark and vector meson channels can induce a diquark BEC-BCS crossover in color superconductor, and in the BEC region the chromomagnetic instability is fully cured and the ground state is a uniform phase.Comment: 18 pages, 15 figures. V2: typos corrected, references added. V3: typos in Appendix B correcte

Numerical Portrait of a Relativistic BCS Gapped Superfluid

We present results of numerical simulations of the 3+1 dimensional Nambu - Jona-Lasinio (NJL) model with a non-zero baryon density enforced via the introduction of a chemical potential mu not equal to 0. The triviality of the model with a number of dimensions d>=4 is dealt with by fitting low energy constants, calculated analytically in the large number of colors (Hartree) limit, to phenomenological values. Non-perturbative measurements of local order parameters for superfluidity and their related susceptibilities show that, in contrast to the 2+1 dimensional model, the ground-state at high chemical potential and low temperature is that of a traditional BCS superfluid. This conclusion is supported by the direct observation of a gap in the dispersion relation for 0.5<=(mu a)<=0.85, which at (mu a)=0.8 is found to be roughly 15% the size of the vacuum fermion mass. We also present results of an initial investigation of the stability of the BCS phase against thermal fluctuations. Finally, we discuss the effect of splitting the Fermi surfaces of the pairing partners by the introduction of a non-zero isospin chemical potential.Comment: 41 pages, 19 figures, uses axodraw.sty, v2: minor typographical correction

Non-Compact QED_3 with N_f=1 and N_f=4

We present numerical results for non-compact three-dimensional QED for numbers of flavors N_f=1 and N_f=4.In particular, we address the issue of whether chiral symmetry is spontaneously broken in the continuum limit, and obtain a positive answer for N_f=1, with a dimensionless condensate estimated to be beta^2 ~= O(10^-3), implying that the critical number of flavors N_fc>1. We also compare the N_f=1 and N_f=4 models by analysing the transition from strong to weak coupling behaviour using an equation of state based on a continuous phase transition. While some qualitative differences emerge, it appears difficult to determine whether N_f=4 lies above or below N_fc.Comment: 19 pages, 10 figure