Density matrix renormalization on random graphs and the quantum spin-glass transition

Abstract

The density matrix renormalization group (DMRG) has been extended to study quantum phase transitions on random graphs of fixed connectivity. As a relevant example, we have analysed the random Ising model in a transverse field. If the couplings are random, the number of retained states remains reasonably low even for large sizes. The resulting quantum spin-glass transition has been traced down for a few disorder realizations, through the careful measurement of selected observables: spatial correlations, entanglement entropy, energy gap and spin-glass susceptibility, among others.