Entanglement entropy and multifractality at localization transitions

Abstract

The von Neumann entanglement entropy is a useful measure to characterize a quantum phase transition. We investigate the non-analyticity of this entropy at disorder-dominated quantum phase transitions in non-interacting electronic systems. At these critical points, the von Neumann entropy is determined by the single particle wave function intensity which exhibits complex scale invariant fluctuations. We find that the concept of multifractality is naturally suited for studying von Neumann entropy of the critical wave functions. Our numerical simulations of the three dimensional Anderson localization transition and the integer quantum Hall plateau transition show that the entanglement at these transitions is well described using multifractal analysis.

v3, 5 pages, published version

References in corpus (16)

• Entanglement Entropy and Quantum Field Theory
• Entanglement in quantum critical phenomena
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Entanglement in a simple quantum phase transition
• Scaling Theory of the Integer Quantum Hall Effect
• Quantum Phase Transitions and Bipartite Entanglement
• Quantum Entanglement in Fermionic Lattices
• Entanglement entropy of random quantum critical points in one dimension
• Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
• Entanglement entropy in fermionic Laughlin states
• Reconciling Conductance Fluctuations and the Scaling Theory of Localization
• Infinite-Randomness Fixed Points for Chains of Non-Abelian Quasiparticles
• Dimensional dependence of the metal-insulator transition
• Replacing energy by von Neumann entropy in quantum phase transitions
• Quantum Hall plateau transition in the lowest Landau level of disordered graphene

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