Exact diagonalization plus renormalization-group theory: Accurate method for a one-dimensional superfluid-insulator-transition study

We use the exact-diagonalization results for a one-dimensional finite-size boson Hubbard-like Hamiltonians to initialize the renormalization-group equations in the vicinity of the superfluid-insulator transition and demonstrate that this provides a rather accurate method of extrapolation of the finite-size results to larger system sizes, and in particular, pinpointing the critical parameters of the Hamiltonians. With our approach we reproduce with the accuracy ∼2.5% the known analytical result for the transition point in the half-filled system of hard-core bosons, obtain with a controllable accuracy the critical ratio (t/U${)}_{\mathit{c}}$=0.304±0.002 for the boson Hubbard model, and find out that, in contrast to the general belief, the reduced Hamiltonian (with the constraint that the site occupation numbers be less than 3) is far from being a good approximation to the full model. © 1996 The American Physical Society.