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Register a new userDual Formulation and Phase Diagram of Lattice QCD in the Strong Coupling Regime
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We present the computation of invariants that arise in the strong coupling expansion of lattice QCD. These invariants are needed for Monte Carlo simulations of Lattice QCD with staggered fermions in a dual, color singlet representation. This formulation is in particular useful to tame the finite density sign problem. The gauge integrals in this limiting case $betarightarrow 0$ are well known, but the gauge integrals needed to study the gauge corrections are more involved. We discuss a method to evaluate such integrals. The phase boundary of lattice QCD for staggered fermions in the $mu_B-T$ plane has been established in the strong coupling limit. We present numerical simulations away from the strong coupling limit, taking into account the higher order gauge corrections via plaquette occupation numbers. This allows to study the nuclear and chiral transition as a function of $beta$.
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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 present results for lattice QCD in the limit of infinite gauge coupling on a discrete spatial but continuous Euclidean time lattice. A worm type Monte Carlo algorithm is applied in order to sample two-point functions which gives access to the measurement of mesonic temporal correlators. The continuous time limit, based on sending $N_taurightarrow infty$ and the bare anistotropy to infinity while fixing the temperature in a non-perturbative setup, has various advantages: the algorithm is sign problem free, fast, and accumulates high statistics for correlation functions. Even though the measurement of temporal correlators requires the introduction of a binning in time direction, this discretization can be chosen to be by orders finer compared to discrete computations. For different spatial volumes, temporal correlators are measured at zero spatial momentum for a variety of mesonic operators. They are fitted to extract the pole masses and corresponding particles as a function of the temperature. We conclude discussing the possibility to extract transport coefficients from these correlators.
We investigate the Polyakov loop effects on the QCD phase diagram by using the strong-coupling (1/g^2) expansion of the lattice QCD (SC-LQCD) with one species of unrooted staggered quark, including O}(1/g^4) effects. We take account of the effects of Polyakov loop fluctuations in Weiss mean-field approximation (MFA), and compare the results with those in the Haar-measure MFA (no fluctuation from the mean-field). The Polyakov loops strongly suppress the chiral transition temperature in the second-order/crossover region at small chemical potential, while they give a minor modification of the first-order phase boundary at larger chemical potential. The Polyakov loops also account for a drastic increase of the interaction measure near the chiral phase transition. The chiral and Polyakov loop susceptibilities have their peaks close to each other in the second-order/crossover region. In particular in Weiss MFA, there is no indication of the separated deconfinement transition boundary from the chiral phase boundary at any chemical potential. We discuss the interplay between the chiral and deconfinement dynamics via the bare quark mass dependence of susceptibilities.
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.
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.
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