Calculation of multi-fractal dimensions in spin chains.

It was demonstrated in Atas & Bogomolny (2012 Phys. Rev. E 86, 021104) that the ground-state wave functions for a large variety of one-dimensional spin- models are multi-fractals in the natural spin-z basis. We present here the details of analytical derivations and numerical confirmations of this statement.

Distribution of the ratio of consecutive level spacings in random matrix ensembles.

We derive expressions for the probability distribution of the ratio of two consecutive level spacings for the classical ensembles of random matrices. This ratio distribution was recently introduced to study spectral properties of many-body problems, as, contrary to the standard level spacing distributions, it does not depend on the local density of states. Our Wigner-like surmises are shown to be very accurate when compared to numerics and exact calculations in the large matrix size limit. Quantitative improvements are found through a polynomial expansion. Examples from a quantum many-body lattice model and from zeros of the Riemann zeta function are presented.

Multifractality of eigenfunctions in spin chains.

We investigate different one-dimensional quantum spin-1/2 chain models, and by combining analytical and numerical calculations we prove that their ground state wave functions in the natural spin basis are multifractals with, in general, nontrivial fractal dimensions.