Hubbard Model and Lüscher fermions

Recently a new type of algorithms for numerical simulations of models with dynamical fermions has been proposed by M. Lüscher [1]. The idea is based on the approximation of a fermionic determinant by the path integral over some number of bosonic fields, which allows ones to elegantly avoid the main difficulty coming from the nonlocality of the fermionic determinant. The complexity of a sweep of the Lüscher algorithm is proportional to the volume of the system and in this respect it wins in comparison with the standard hybrid Monte Carlo [2]. Of course, what is interesting in practice is a comparison of the computer cost needed to produce independent configurations which is the product of the sweep cost and the autocorrelation time. Therefore the crucial question is how the autocorrelation time depends on the volume of the system. Contrary to the sweep time the autocorrelation time can strongly depend on the external parameters. Therefore it is particularly interesting to test the dependence of the autocorrelation time on the various interesting physical parameters. Recent results obtained in QCD are rather promising showing that the computational cost needed to obtain independent configurations is comparable to the standard HMC algorithms [3]. In this letter we present new results of numerical simulations of the Hubbard Model using the Lüscher method and compare them to standard methods in context of the algorithmical complexity. This is a continuation of our contribution to the proceedings Lattice 95 where we presented preliminary results [4]. In particular, we noted there possible improvements which reduce autocorrelation times. Here, we study the errors introduced by the bosonic approximation and compare dynamical properties of the multiboson algorithm with the simple exact algorithm.