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Register a new userGauge Corrections to Strong Coupling Lattice QCD on Anisotropic Lattices
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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.
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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.
Lattice QCD with staggered fermions at strong coupling has long been studied in a dual representation to circumvent the finite baryon density sign problem. Monte Carlo simulations at finite temperature and density require anisotropic lattices. Recent results that established the non-perturbative functional dependence between the bare anisotropy $gamma$ and the physical anisotropy $a_s/a_t$ in the chiral limit are now extended to finite quark mass. We illustrate how the calibration of the anisotropy works and discuss the consequences of the anisotropy on thermodynamic observables. We also show first results on the energy density and pressure in the QCD phase diagram in the strong coupling regime.
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 $O(beta)$.
The lowest-lying glueballs are investigated in lattice QCD using $N_f=2$ clover Wilson fermion on anisotropic lattices. We simulate at two different and relatively heavy quark masses, corresponding to physical pion mass of $m_pisim 938$ MeV and $650$ MeV. The quark mass dependence of the glueball masses have not been investigated in the present study. Only the gluonic operators built from Wilson loops are utilized in calculating the corresponding correlation functions. In the tensor channel, we obtain the ground state mass to be 2.363(39) GeV and 2.384(67) GeV at $m_pisim 938$ MeV and $650$ MeV, respectively. In the pseudoscalar channel, when using the gluonic operator whose continuum limit has the form of $epsilon_{ijk}TrB_iD_jB_k$, we obtain the ground state mass to be 2.573(55) GeV and 2.585(65) GeV at the two pion masses. These results are compatible with the corresponding results in the quenched approximation. In contrast, if we use the topological charge density as field operators for the pseudoscalar, the masses of the lowest state are much lighter (around 1GeV) and compatible with the expected masses of the flavor singlet $qbar{q}$ meson. This indicates that the operator $epsilon_{ijk}TrB_iD_jB_k$ and the topological charge density couple rather differently to the glueball states and $qbar{q}$ mesons. The observation of the light flavor singlet pseudoscalar meson can be viewed as the manifestation of effects of dynamical quarks. In the scalar channel, the ground state masses extracted from the correlation functions of gluonic operators are determined to be around 1.4-1.5 GeV, which is close to the ground state masses from the correlation functions of the quark bilinear operators. In all cases, the mixing between glueballs and conventional mesons remains to be further clarified in the future.
We present our final results of the charmonium spectrum in quenched QCD on anisotropic lattices. Simulations are made with the plaquette gauge action and a tadpole improved clover quark action employing $xi = a_s/a_t = 3$. We calculate the spectrum of S- and P-states and their excitation, and study the scaling behavior of mass splittings. Comparison is made with the experiment and previous lattice results. The issue of hyperfine splitting for different choices of the clover coefficients obtained by Klassen is discussed.
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