Stochastic projection of the ground state of strongly correlated electrons

Abstract

An overview is presented of Green’s function Monte Carlo methods which have been applied to the two-dimensional t — J model, a simple quantum lattice-gas model which captures strong electron correlations. Exact diagonalization methods are restricted to very small size systems which do not allow extrapolation to the thermodynamic limit. On the other hand, world-line Monte Carlo simulation methods suffer from the fact that the antisymmetric nature of the amplitudes for fermions makes the simulation error grow exponentially with system size. Thus, in straightforward applications of simulation techniques or in exact diagonalization techniques the required computer time grows exponentially with system size. We have developed projection methods similar to the Green’s function Monte Carlo technique which can be used to extract the many-body ground state where the above mentioned problems can be kept under control. This technique reproduces all known exact diagonalization results on smaller size systems and it can be applied on significantly larger size lattices. Using this method, the motion of a hole, the hole-binding and the phase diagram of the t — J model have been studied. Among other important results, it has been found that there is phase separation in the physical region of the model. The relevance of the phase diagram of the model to the physics of the cuprate superconductors and the role of additional terms, which need to be added to the model in order to describe the environment experienced by the electrons in the real materials, are briefly discussed.