Quantum Monte-Carlo simulations of correlated bosonic and fermionic systems

We review recent results of quantum Monte Carlo simulations applied to correlated electronic and bosonic systems. We concentrate on three subjects. 1) Using a recently developed hybrid quantum Monte-Carlo algorithm we investigate the excitation spectra of the one-dimensional t - J model. Our results give strong numerical support for the existence of antiholons, which along with spinons and holons correspond to the elementary excitations of this model. 2) Very recently, it was experimentally demonstrated, that it is possible to attain temperatures low enough, such that degenerate quantum gases can be studied in magneto-optical traps, the most prominent example being Bose-Einstein condensation of alkali atoms. Under the action of a periodic potential created by interfering laser beams, such systems can be brought to a strongly correlated state. We present numerical simulations in one-dimension in order to understand theses new states of matter. 3) Taking the step from one to two and three dimensions poses a formidable numerical challenge. In particular for fermionic models the quantum Monte Carlo method suffers from the so-called sign problem which renders simulations exponentially expensive in CPU time as a function of inverse temperature at lattice size. We show that by considering multi-flavored models this problem is reduced and in some special cases altogether removed.