Bose-glass to Superfluid transition in the three-dimensional Bose-Hubbard Model

We present a Monte Carlo study of the Bose-glass to superfluid transition in the three-dimensional Bose-Hubbard model. Simulations are performed on the classical (3 + 1) dimensional link-current representation using the geometrical worm algorithm. Finite-size scaling analysis (on lattices as large as 16x16x16x512 sites) of the superfluid stiffness and the compressibility is consistent with a value of the dynamical critical exponent z = 3, in agreement with existing scaling and renormalization group arguments that z = d. We find also a value of $\nu = 0.70(12)$ for the correlation length exponent, satisfying the relation $\nu >= 2/d$. However, a detailed study of the correlation functions, C(r, tau), at the quantum critical point are not consistent with this value of z. We speculate that this discrepancy could be due to the fact that the correlation functions have not reached their true asymptotic behavior because of the relatively small spatial extent of the lattices used in the present study.Comment: 9 pages, 8 figures, submitted to PR

Finite Size Scaling of the Spin Stiffness of the Antiferromagnetic S=1/2 XXZ chain

We study the finite size scaling of the spin stiffness for the one-dimensional s=1/2 quantum antiferromagnet as a function of the anisotropy parameter Delta.Previous Bethe ansatz results allow a determination of the stiffness in the thermodynamic limit. The Bethe ansatz equations for finite systems are solvable even in the presence of twisted boundary conditions, a fact we exploit to determine the stiffness exactly for finite systems allowing for a complete determination of the finite size corrections. Relating the stiffness to thermodynamic quantities we calculate the temperature dependence of the susceptibility and its finite size corrections at T=0. A Luttinger liquid approach is used to study the finite size corrections using renormalization group techniques and the results are compared to the numerically exact results obtained using the Bethe ansatz equations. Both irrelevant and marginally irrelevant cases are considered