Test of Conformal Invariance in One-Dimensional Quantum Liquid with Long-Range Interaction

We numerically study the momentum distribution of one-dimensional Bose and Fermi systems with long-range interaction $g/r^2$ for the ``special'' values $g= -\frac{1}{2}, 0, 4$, singled out by random matrix theory. The critical exponents are shown to be independent of density and in excellent agreement with estimates obtained from $c=1$ conformal finite-size scaling analysis.Comment: 25 page

Using entanglement to discern phases in the disordered one-dimensional Bose-Hubbard model

We perform a matrix product state based density matrix renormalisation group analysis of the phases for the disordered one-dimensional Bose-Hubbard model. For particle densities N/L = 1, 1/2 and 2 we show that it is possible to obtain a full phase diagram using only the entanglement properties, which come "for free" when performing an update. We confirm the presence of Mott insulating, superfluid and Bose glass phases when N/L = 1 and 1/2 (without the Mott insulator) as found in previous studies. For the N/L = 2 system we find a double lobed superfluid phase with possible reentrance.Comment: 6 pages, 4 figure

Finite-Size Scaling of the Level Compressibility at the Anderson Transition

We compute the number level variance $\Sigma_{2}$ and the level compressibility $\chi$ from high precision data for the Anderson model of localization and show that they can be used in order to estimate the critical properties at the metal-insulator transition by means of finite-size scaling. With $N$, $W$, and $L$ denoting, respectively, system size, disorder strength, and the average number of levels in units of the mean level spacing, we find that both $\chi(N,W)$ and the integrated $\Sigma_{2}$ obey finite-size scaling. The high precision data was obtained for an anisotropic three-dimensional Anderson model with disorder given by a box distribution of width $W/2$. We compute the critical exponent as $\nu \approx 1.45 \pm 0.12$ and the critical disorder as $W_{\rm c} \approx 8.59 \pm 0.05$ in agreement with previous transfer-matrix studies in the anisotropic model. Furthermore, we find $\chi\approx 0.28 \pm 0.06$ at the metal-insulator transition in very close agreement with previous results.Comment: Revised version of paper, to be published: Eur. Phys. J. B (2002