The Renyi Entropy and the Multifractal Spectrum of Systems Near the Localization Transition

Abstract

We show that the Rényi entropies of single particle, extended wave functions for disordered systems contain information about the multifractal spectrum. It is shown for moments of the Rényi entropy, $S_n$, where $|n|<1$, it is possible to extract universal information about the multifractility of such systems. This is shown through a generic calculation and then illustrated through two example models. We find good agreement between our analytic formula and numerical simulations of the two test models. Our formalism is easily extendable to generic non-interacting fermion models. It is also suggested that recent experimental advances in measuring the multifractal spectrum might allow some moments of the Rényi entropy to be measured.

v2,5 pages, 2 figures

References in corpus (8)

• Anderson Transitions
• Localization of ultrasound in a three-dimensional elastic network
• Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
• Entanglement Entropy in the O(N) model
• Universal entanglement entropy in 2D conformal quantum critical points
• Entanglement entropy and multifractality at localization transitions
• Universal Behavior of Entanglement in 2D Quantum Critical Dimer Models
• Scaling of von Neumann entropy at the Anderson transition

Cited by in corpus (5)

• Drive Induced Delocalization in Aubry-André Model
• Signatures of metal-insulator and topological phase transitions in the entanglement of one-dimensional disordered fermions
• Multi-fractality of the entanglement Hamiltonian eigen-modes
• Single-particle Entanglement of the Entanglement Hamiltonian Eigen-modes
• Localization transitions in quadratic systems without quantum chaos