Applications of Cluster Perturbation Theory Using Quantum Monte Carlo Data

We study cluster perturbation theory [Phys. Rev. Lett. \textbf{84}, 522 (2000)] when auxiliary field quantum Monte Carlo method is used for solving the cluster hamiltonian. As a case study, we calculate the spectral functions of the Hubbard model in one and two dimensions and compare our results for the spectral functions to results obtained using exact diagonalization to solve the cluster hamiltonian. The main advantage of using quantum Monte Carlo results as a starting point is that the initial cluster size can be taken to be considerably larger and hence potentially capture more of the relevant physics. The drawback is that quantum Monte Carlo methods yield results at {\it imaginary} times with stochastic errors.