Mott-insulator-superfluid-liquid transition in a one-dimensional bosonic Hubbard model: Quantum Monte Carlo method

The values of the insulator gap Delta in one-dimensional systems of interacting bosons described by the Hubbard Hamiltonian are calculated at low temperatures by the quantum world-line Monte Carlo algorithm. The dependence of Delta on the size of the system, the temperature, and the parameters of the model is investigated. It is shown that a chain with N-a=50 sites is already sufficient to estimate the thermodynamic value of the critical quantity (t/U)(c) for which a transition from the insulator into the superfluid state occurs in a commensurate system. To within the computational error, this value, (t/U)(c)=0.300+/-0.005, agrees with the value (t/U)(c)=0.304+/-0.002 obtained previously by the combined ''exact diagonalization + renormalization-group analysis'' method. The characteristic Kosterlitz-Thouless behavior of the insulator gap is demonstrated near the critical region: Delta similar to exp[-b(1-t/t(c))(-1/2)]. (C) 1996 American Institute of Physics.