Entanglement entropy and multifractality at localization transitions

Details Entanglement entropy and multifractality at localization transitions Entanglement entropy and multifractality at localization transitions

2007-10-09

arxiv.org/abs/0710.1871v3

Phys. Rev. B 77, 014208 (2008)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

v3, 5 pages, published version

Scientific paper

10.1103/PhysRevB.77.014208

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.

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