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

An exact-diagonalization study of rare events in disordered conductors

We determine the statistical properties of wave functions in disordered quantum systems by exact diagonalization of one-, two- and quasi-one dimensional tight-binding Hamiltonians. In the quasi-one dimensional case we find that the tails of the distribution of wave-function amplitudes are described by the non-linear sigma-model. In two dimensions, the tails of the distribution function are consistent with a recent prediction based on a direct optimal fluctuation method.Comment: 13 pages, 5 figure

Leaf-to-leaf distances and their moments in finite and infinite m-ary tree graphs

We study the leaf-to-leaf distances on full and complete m-ary graphs using a recursive approach. In our formulation, leaves are ordered along a line. We find explicit analytical formulae for the sum of all paths for arbitrary leaf-to-leaf distance r as well as the average path lengths and the moments thereof. We show that the resulting explicit expressions can be recast in terms of Hurwitz-Lerch transcendants. Results for periodic trees are also given. For incomplete random binary trees, we provide first results by numerical techniques; we find a rapid drop of leaf-to-leaf distances for large r.Comment: 10 pages, 7 figure

Localisation and finite-size effects in graphene flakes

We show that electron states in disordered graphene, with an onsite potential that induces inter-valley scattering, are localised for all energies at disorder as small as of the band width of clean graphene. We clarify that, in order for this Anderson-type localisation to be manifested, graphene flakes of size or larger are needed. For smaller samples, due to the surprisingly large extent of the electronic wave functions, a regime of apparently extended (or even critical) states is identified. Our results complement earlier studies of macroscopically large samples and can explain the divergence of results for finite-size graphene flakes

Hamiltonian Multivector Fields and Poisson Forms in Multisymplectic Field Theory

We present a general classification of Hamiltonian multivector fields and of Poisson forms on the extended multiphase space appearing in the geometric formulation of first order classical field theories. This is a prerequisite for computing explicit expressions for the Poisson bracket between two Poisson forms.Comment: 50 page

Cooper pair delocalization in disordered media

We discuss the effect of disorder on the coherent propagation of the bound state of two attracting particles. It is shown that a result analogous to the Anderson theorem for dirty superconductors is also valid for the Cooper problem, namely, that the pair wave function is extended beyond the single-particle localization length if the latter is large. A physical justification is given in terms of the Thouless block-scaling picture of localization. These arguments are supplemented by numerical simulations. With increasing disorder we find a transition from a regime in which the interaction delocalizes the pair to a regime in which the interaction enhances localization.Comment: 5 pages, RevTex with 2 figures include

Spin noise spectroscopy in GaAs (110) quantum wells: Access to intrinsic spin lifetimes and equilibrium electron dynamics

In this letter, the first spin noise spectroscopy measurements in semiconductor systems of reduced effective dimensionality are reported. The non-demolition measurement technique gives access to the otherwise concealed intrinsic, low temperature electron spin relaxation time of n-doped GaAs (110) quantum wells and to the corresponding low temperature anisotropic spin relaxation. The Brownian motion of the electrons within the spin noise probe laser spot becomes manifest in a modification of the spin noise line width. Thereby, the spatially resolved observation of the stochastic spin polarization uniquely allows to study electron dynamics at equilibrium conditions with a vanishing total momentum of the electron system