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 μ, using the same 12³×24 lattice, bare gauge coupling, and pion mass in cut-off units as a previous study (S. Hands, S. Kim, J.I. Skullerud, Phys. Rev. D 81, 091502(R) (2010)) 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 μ 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 μ above onset.     

Bottomonium above deconfinement in lattice nonrelativistic QCD

We study the temperature dependence of bottomonium for temperatures in the range 0.4T(c) < T < 2.1T(c), using nonrelativistic dynamics for the bottom quark and full relativistic lattice QCD simulations for Nf = 2 light flavors on a highly anisotropic lattice. We find that the Υ is insensitive to the temperature in this range, while the χb propagators show a crossover from the exponential decay characterizing the hadronic phase to a power-law behavior consistent with nearly free dynamics at T ? 2T(c).     

Diquark condensation in dense adjoint matter

We study SU(2) lattice gauge theory at non-zero chemical potential with one staggered quark flavor in the adjoint representation. In this model the fermion determinant, although real, can be both positive and negative. We have performed numerical simulations using both hybrid Monte Carlo and two-step multibosonic algorithms, the latter being capable of exploring sectors with either determinant sign. We find that the positive determinant sector behaves like a two-flavor theory, with the chiral condensate rotating into a two-flavor diquark condensate for , implying a superfluid ground state. Good agreement is found with analytical predictions made using chiral perturbation theory. In the ‘full’ model there is no sign of either onset of baryon density or diquark condensation for the range of chemical potentials we have considered. The impact of the sign problem has prevented us from exploring the true onset transition and the mode of diquark condensation, if any, for this model. Received: 28 September 2001 / Published online: 23 November 2001     

Non-relativistic spectrum of two-color QCD at non-zero baryon density

The heavy quarkonium spectrum of Two Color QCD (QC₂D) at non-zero quark chemical potential μ and temperature T   with μ/T?1$\mu /T?1$ has been calculated in both S- and P-wave channels using a lattice non-relativistic formulation of QC₂D. As μ is varied, the quarkonium spectra reveal three separate regions, corroborating previous findings that there are three distinct physical regimes of QC₂D at low temperature and high baryon density: hadronic matter, quark/quarkyonic matter, and deconfined matter. The results are interpreted in terms of the formation of heavy-light Qq states in the two-color baryonic medium.     

Quarks and gluons in dense two-colour QCD

We compute quark and gluon propagators in 2-colour QCD at large baryon chemical potential μ. The gluon propagator is found to be antiscreened at intermediate μ and screened at large μ. The quark propagator is drastically modified in the superfluid region as a result of the formation of a superfluid gap.     

Hadron spectrum in a two-colour baryon-rich medium

The hadron spectrum of SU(2)$\mathrm{SU}(2)$ lattice gauge theory with two flavours of Wilson quark is studied on an ⁸³×16$8^3\times 16$ lattice using all-to-all propagators, with particular emphasis on the dependence on quark chemical potential μ. As μ is increased from zero the diquark states with non-zero baryon number B   respond as expected, while states with B=0$B=0$ remain unaffected, until the onset of non-zero baryon density at μ=mπ/2$\mu =m_{\pi }/2$. Post onset the pi-meson mass increases in accordance with chiral perturbation theory while the rho becomes lighter. In the diquark sector a Goldstone state associated with a superfluid ground state can be identified. A further consequence of superfluidity is an approximate degeneracy between mesons and baryons with the same spacetime and isospin quantum numbers. Finally we find tentative evidence for the binding of states with kaon quantum numbers within the baryonic medium.     

Quark–gluon vertex in general kinematics

We compute the quark–gluon vertex in quenched lattice QCD in the Landau gauge, using an off-shell mean-field -improved fermion action. The Dirac-vector part of the vertex is computed for arbitrary kinematics. We find a substantial infrared enhancement of the interaction strength regardless of the kinematics.     

Numerical study of dense adjoint matter in two color QCD

We identify the global symmetries of SU(2) lattice gauge theory with N flavors of staggered fermion in the presence of a quark chemical potential , for fermions in both fundamental and adjoint representations, and anticipate likely patterns of symmetry breaking at both low and high densities. Results from numerical simulations of the model with N = 1 adjoint flavor on a lattice are presented, using both hybrid Monte Carlo and Two-Step Multi-Boson algorithms. It is shown that the sign of the fermion determinant starts to fluctuate once the model enters a phase with non-zero baryon charge density. HMC simulations are not ergodic in this regime, but TSMB simulations retain ergodicity even in the dense phase, and in addition appear to show superior decorrelation. The HMC results for the equation of state and the pion mass show good quantitative agreement with the predictions of chiral perturbation theory, which should hold only for . The TSMB results incorporating the sign of the determinant support a delayed onset transition, consistent with the pattern of symmetry breaking expected for N = 1. Received: 20 June 2000 / Published online: 31 August 2000     

Deconfinement in dense two-color QCD

We study SU(2) lattice gauge theory with two flavors of Wilson fermion at non-zero chemical potential μ and low temperature on a 8³×16 system. We identify three régimes along the μ-axis. For μ≲m_π/2 the system remains in the vacuum phase and all physical observables considered remain essentially unchanged. The intermediate régime is characterised by a non-zero diquark condensate and an associated increase in the baryon density, consistent with what is expected for Bose–Einstein condensation of tightly bound diquarks. We also observe screening of the static quark potential here. In the high-density deconfined régime we find a non-zero Polyakov loop and a strong modification of the gluon propagator, including significant screening in the magnetic sector in the static limit, which must have a non-perturbative origin. The behaviour of thermodynamic observables and the superfluid order parameter are consistent with a Fermi surface disrupted by a BCS diquark condensate. The energy per baryon as a function of μ exhibits a minimum in the deconfined régime, implying that macroscopic objects such as stars formed in this theory are largely composed of quark matter.