TY - JOUR
T1 - Entanglement entropy and multifractality at localization transitions
AU - Jia, Xun
AU - Subramaniam, Arvind R.
AU - Gruzberg, Ilya A.
AU - Chakravarty, Sudip
PY - 2008/1/25
Y1 - 2008/1/25
N2 - The von Neumann entanglement entropy is a useful measure to characterize a quantum phase transition. We investigate the nonanalyticity of this entropy at disorder-dominated quantum phase transitions in noninteracting 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.
AB - The von Neumann entanglement entropy is a useful measure to characterize a quantum phase transition. We investigate the nonanalyticity of this entropy at disorder-dominated quantum phase transitions in noninteracting 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.
UR - http://www.scopus.com/inward/record.url?scp=38549094057&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=38549094057&partnerID=8YFLogxK
U2 - 10.1103/PhysRevB.77.014208
DO - 10.1103/PhysRevB.77.014208
M3 - Article
AN - SCOPUS:38549094057
SN - 1098-0121
VL - 77
JO - Physical Review B - Condensed Matter and Materials Physics
JF - Physical Review B - Condensed Matter and Materials Physics
IS - 1
M1 - 014208
ER -