Quantum Monte Carlo study of a single hole in a quantum antiferromagnet

Using the standard quantum Monte Carlo technique for the Hubbard model, I present here a numerical investigation of the hole propagation in a quantum antiferromagnet. The calculation is very well stabilized, using selected-size systems and a special choice of the trial wave function that satisfies the "closed-shell condition" in the presence of an arbitrarily weak Zeeman magnetic field. First it is shown that the presence of this magnetic field does not affect the thermodynamic properties of the half-filled system. Then I use the same selected sizes for the one-hole ground state. I investigate the question of vanishing or nonvanishing quasiparticle weight, in order to clarify whether the Mott insulator behaves as a conventional insulator with an upper and lower Hubbard band. By comparing the present finite-size scaling with several techniques that predict a finite quasiparticle weight, the data seem more consistent with a vanishing quasiparticle weight, i.e., the Mott-Hubbard insulator should be characterized by nontrivial excitations that cannot be interpreted in a simple picture. However, one cannot exclude, based only on numerical grounds, a very small but nonvanishing quasiparticle weight. In the last part I give some theoretical arguments to explain the results of the Monte Carlo simulation.