Loop algorithms for quantum simulations of fermion models on lattices

Two cluster algorithms, based on constructing and flipping loops, are presented for worldline quantum Monte Carlo simulations of fermions and are tested on the one-dimensional repulsive Hubbard model. We call these algorithms the loop-flip and loop-exchange algorithms. For these two algorithms and the standard worldline algorithm, we calculated the autocorrelation times for various physical quantities and found that the ordinary worldline algorithm, which uses only local moves, suffers from very long correlation times that makes not only the estimate of the error difficult but also the estimate of the average values themselves difficult. These difficulties are especially severe in the low-temperature, large-$U$ regime. In contrast, we find that new algorithms, when used alone or in combinations with themselves and the standard algorithm, can have significantly smaller autocorrelation times, in some cases being smaller by three orders of magnitude. The new algorithms, which use non-local moves, are discussed from the point of view of a general prescription for developing cluster algorithms. The loop-flip algorithm is also shown to be ergodic and to belong to the grand canonical ensemble. Extensions to other models and higher dimensions is briefly discussed.Comment: 36 pages, RevTex ver.

Nuclear equation of state at high density and the properties of neutron stars

We discuss the relativistic nuclear equation of state (EOS) using a relativistic transport model in heavy-ion collisions. From the baryon flow for $Au + Au$ systems at SIS to AGS energies and above we find that the strength of the vector potential has to be reduced moderately at high density or at high relative momenta to describe the flow data at 1-10 A GeV. We use the same dynamical model to calculate the nuclear EOS and then employ this to calculate the gross structure of the neutron star considering the core to be composed of neutrons with an admixture of protons, electrons, muons, sigmas and lambdas at zero temperature. We then discuss these gross properties of neutron stars such as maximum mass and radius in contrast to the observational values.Comment: 17 pages, 5 figures, to be published in Phy. Rev.

Quark Hadron Phase Transition and Hybrid Stars

We investigate the properties of hybrid stars consisting of quark matter in the core and hadron matter in outer region. The hadronic and quark matter equations of state are calculated by using nonlinear Walecka model and chiral colour dielectric (CCD) model respectively. We find that the phase transition from hadron to quark matter is possible in a narrow range of the parameters of nonlinear Walecka and CCD models. The transition is strong or weak first order depending on the parameters used. The EOS thus obtained, is used to study the properties of hybrid stars. We find that the calculated hybrid star properties are similar to those of pure neutron stars.Comment: 25 pages in LaTex and 9 figures available on request, IP/BBSR/94-3