Agradecimentos: The authors would like to acknowledge useful discussions with S. Kehrein, S. Gopalakrishnan, E. Miranda, and D. Huse. P.T. and G.R. are grateful for support from NSF through Grant No. DMR-1410435, as well as the Institute of Quantum Information and Matter, an NSF Frontier center funded by the Gordon and Betty Moore Foundation, and the Packard Foundation. V.L.Q. acknowledges financial support from FAPESP, through Grants No. 2012/17082-7 and No. 2009/17531-3 Ver menos

Abstract: The flow-equation method was proposed by Wegner as a technique for studying interacting systems in one dimension. Here, we apply this method to a disordered one-dimensional model with power-law decaying hoppings. This model presents a transition as function of the decaying exponent alpha. We derive the flow equations and the evolution of single-particle operators. The flow equation reveals the delocalized nature of the states for alpha < 1/2. Additionally, in the regime alpha > 1/2, we present a strong-bond renormalization group structure based on iterating the three-site clusters, where we solve the flow equations perturbatively. This renormalization group approach allows us to probe the critical point (alpha = 1). This method correctly reproduces the critical level-spacing statistics and the fractal dimensionality of the eigenfunctions Ver menos