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Register a new userChiral and deconfinement transitions in strong coupling lattice QCD
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We investigate the QCD phase diagram based on the strong coupling expansion of the lattice QCD with one species of the staggered fermions at finite temperature (T) and chemical potential (mu). We analytically derive an effective potential including both chiral and deconfinement (Z_3) dynamics with finite coupling effects in mean-field approximations. We focus on Polyakov loop properties in whole T-mu plane, and study relations between the chiral and deconfinement crossovers. At a fixed large mu, sequencial rapid variations of the Polyakov loop are observed with increasing T. It is natural to interprete them as the chiral induced and Z_3 induced deconfinement crossovers.
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We investigate the QCD phase diagram by using the strong-coupling expansion of the lattice QCD with one species of staggered fermion and the Polyakov loop effective action at finite temperature (T) and quark chemical potential (mu). We derive an analytic expression of effective potential Feff including both the chiral (U(1)) and the deconfinement (Z_Nc) dynamics with finite coupling effects in the mean-field approximation. The Polyakov loop increasing rate (dl/dT) is found to have two peaks as a function of T for small quark masses. One of them is the chiral-induced peak associated with the rapid decrease of the chiral condensate. The temperature of the other peak is almost independent of the quark mass or chemical potential, and this peak is interpreted as the Z_Nc-induced peak.
Anisotropic lattice spacings are mandatory to reach the high temperatures where chiral symmetry is restored in the strong coupling limit of lattice QCD. Here, we propose a simple criterion for the nonperturbative renormalisation of the anisotropy coupling in strongly-coupled SU($N$) or U($N$) lattice QCD with massless staggered fermions. We then compute the renormalised anisotropy, and the strong-coupling analogue of Karschs coefficients (the running anisotropy), for $N=3$. We achieve high precision by combining diagrammatic Monte Carlo and multi-histogram reweighting techniques. We observe that the mean field prediction in the continuous time limit captures the nonperturbative scaling, but receives a large, previously neglected correction on the unit prefactor. Using our nonperturbative prescription in place of the mean field result, we observe large corrections of the same magnitude to the continuous time limit of the static baryon mass, and of the location of the phase boundary associated with chiral symmetry restoration. In particular, the phase boundary, evaluated on different finite lattices, has a dramatically smaller dependence on the lattice time extent. We also estimate, as a byproduct, the pion decay constant and the chiral condensate of massless SU(3) QCD in the strong coupling limit at zero temperature.
We investigate the chiral phase transition in the strong coupling lattice QCD at finite temperature and density with finite coupling effects. We adopt one species of staggered fermion, and develop an analytic formulation based on strong coupling and cluster expansions. We derive the effective potential as a function of two order parameters, the chiral condensate sigma and the quark number density $rho_q$, in a self-consistent treatment of the next-to-leading order (NLO) effective action terms. NLO contributions lead to modifications of quark mass, chemical potential and the quark wave function renormalization factor. While the ratio mu_c(T=0)/Tc(mu=0) is too small in the strong coupling limit, it is found to increase as beta=2Nc/g^2 increases. The critical point is found to move in the lower T direction as beta increases. Since the vector interaction induced by $rho_q$ is shown to grow as beta, the present trend is consistent with the results in Nambu-Jona-Lasinio models. The interplay between two order parameters leads to the existence of partially chiral restored matter, where effective chemical potential is automatically adjusted to the quark excitation energy.
We study the temperature dependence of bottomonium for temperatures in the range $0.4 T_c < T < 2.1 T_c$, using nonrelativistic dynamics for the bottom quark and full relativistic lattice QCD simulations for $N_f=2$ light flavors on a highly anisotropic lattice. We find that the $Upsilon$ is insensitive to the temperature in this range, while the $chi_b$ propagators show a crossover from the exponential decay characterizing the hadronic phase to a power-law behaviour consistent with nearly-free dynamics at $T simeq 2 T_c$.
We present results for lattice QCD with staggered fermions in the limit of infinite gauge coupling, obtained from a worm-type Monte Carlo algorithm on a discrete spatial lattice but with continuous Euclidean time. This is obtained by sending both the anisotropy parameter $xi=a_sigma/a_tau$ and the number of time-slices $N_tau$ to infinity, keeping the ratio $aT=xi/Ntau$ fixed. The obvious gain is that no continuum extrapolation $N_tau rightarrow infty$ has to be carried out. Moreover, the algorithm is faster and the sign problem disappears. We derive the continuous time partition function and the corresponding Hamiltonian formulation. We compare our computations with those on discrete lattices and study both zero and finite temperature properties of lattice QCD in this regime.
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