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Register a new userTowards corrections to the strong coupling limit of staggered lattice QCD
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We report on the first steps of an ongoing project to add gauge observables and gauge corrections to the well-studied strong coupling limit of staggered lattice QCD, which has been shown earlier to be amenable to numerical simulations by the worm algorithm in the chiral limit and at finite density. Here we show how to evaluate the expectation value of the Polyakov loop in the framework of the strong coupling limit at finite temperature, allowing to study confinement properties along with those of chiral symmetry breaking. We find the Polyakov loop to rise smoothly, thus signalling deconfinement. The non-analytic nature of the chiral phase transition is reflected in the derivative of the Polyakov loop. We also discuss how to construct an effective theory for non-zero lattice coupling, which is valid to $O(beta)$.
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Lattice QCD with staggered fermions can be formulated in dual variables to address the finite baryon density sign problem. In the past we have performed simulations in the strong coupling regime, including leading order gauge corrections. In order to vary the temperature for fixed $beta$ it was necessary to introduce a bare anisotropy. In this talk we will extend our work to include results from a non-perturbative determination of the physical anisotropy $a_sigma$/$a_tau = xi(gamma, beta)$, which is necessary to unambiguously locate the critical end point and the first order line of the chiral transition.
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 discuss the QCD phase diagram in the strong coupling limit of lattice QCD by using a new type of mean field coming from the next-to-leading order of the large dimensional expansion. The QCD phase diagram in the strong coupling limit recently obtained by using the monomer-dimer-polymer (MDP) algorithm has some differences in the phase boundary shape from that in the mean field results. As one of the origin to explain the difference, we consider another type of auxiliary field, which corresponds to the point-splitting mesonic composite. Fermion determinant with this mean field under the anti-periodic boundary condition gives rise to a term which interpolates the effective potentials in the previously proposed zero and finite temperature mean field treatments. While the shift of the transition temperature at zero chemical potential is in the desirable direction and the phase boundary shape is improved, we find that the effects are too large to be compatible with the MDP simulation results.
We study the phase diagram of quark matter and nuclear properties based on the strong coupling expansion of lattice QCD. Both of baryon and finite coupling correction are found to have effects to extend the hadron phase to a larger mu direction relative to Tc. In a chiral RMF model with logarithmic sigma potential derived in the strong coupling limit of lattice QCD, we can avoid the chiral collapse and normal and hypernuclei properties are well described.
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.
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