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We study the basic features of the two-dimensional quantum Hubbard Model at half-filling by means of the Luscher algorithm and the algorithm based on direct update of the determinant of the fermionic matrix. We implement the Luscher idea employing the transfer matrix formalism which allows to formulate the problem on the lattice in $(2+1)$ dimensions. We discuss the numerical complexity of the Luscher technique, systematic errors introduced by polynomial approximation and introduce some improvements which reduce long autocorrelations. In particular we show that preconditioning of the fermionic matrix speeds up the algorithm and extends the available range of parameters. We investigate the magnetic and the one-particle properties of the Hubbard Model at half-filling and show that they are in qualitative agreement with the existing Monte Carlo data and the mean-field predictions.
We discuss numerical complexity of the Luscher algorithm applied to the Hubbard Model. In particular we present comparison to a certain algorithm based on direct computation of the fermionic determinant.
Some modifications of the Luscher algorithm, which reduce the autocorelation time, are proposed and tested.
It is believed that fermions in adjoint representation on single site lattice will restore the center symmetry, which is a crucial requirement for the volume independence of large-N lattice gauge theories. We present a perturbative analysis which sup
We present simulation results for the 2-flavour Schwinger model with dynamical overlap fermions. In particular we apply the overlap hypercube operator at seven light fermion masses. In each case we collect sizable statistics in the topological sector
We investigate the neighbourhood of the chiral phase transition in a lattice Nambu--Jona-Lasinio model, using both Monte Carlo methods and lattice Schwinger-Dyson equations.