Geometric entanglement in the Laughlin wave function

We study numerically the geometric entanglement in the Laughlin wave function, which is of great importance in condensed matter physics. The Slater determinant having the largest overlap with the Laughlin wave function is constructed by an iterative algorithm. The logarithm of the overlap, which is...

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Published in:New journal of physics 2017-08, Vol.19 (8), p.83019
Main Authors: Zhang, Jiang-Min, Liu, Yu
Format: Article
Language:English
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03.67.Mn
Condensed matter physics
Electrons
Entanglement
Entropy
fractional quantum Hall effect
geometric measure of entanglement
Helium
Iterative algorithms
Iterative methods
Laughlin wave function
Linear functions
Physics
topological entropy
topological order
Topology
Wave functions
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description We study numerically the geometric entanglement in the Laughlin wave function, which is of great importance in condensed matter physics. The Slater determinant having the largest overlap with the Laughlin wave function is constructed by an iterative algorithm. The logarithm of the overlap, which is a geometric quantity, is then taken as a geometric measure of entanglement. It is found that the geometric entanglement is a linear function of the number of electrons to a good extent. This is especially the case for the lowest Laughlin wave function, namely the one with filling factor of 1/3. Surprisingly, the linear behavior extends well down to the smallest possible value of the electron number, namely, N = 2. The constant term does not agree with the expected topological entropy. In view of previous works, our result indicates that the relation between geometric entanglement and topological entropy is very subtle.
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subjects 03.67.Mn
Condensed matter physics
Electrons
Entanglement
Entropy
fractional quantum Hall effect
geometric measure of entanglement
Helium
Iterative algorithms
Iterative methods
Laughlin wave function
Linear functions
Physics
topological entropy
topological order
Topology
Wave functions
title Geometric entanglement in the Laughlin wave function
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