Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0710.4071 · Physical Review B

Topological entropy of realistic quantum Hall wave functions

Barry Friedman, Gregory Levine

Published Jul 21, 2008• 19 citations
arXivHTMLPDF

Abstract

The entanglement entropy of the incompressible states of a realistic quantum Hall system is studied by direct diagonalization. The subdominant term to the area law, the topological entanglement entropy (which is believed to carry information about topologic order in the ground state), was extracted for filling factors $\ensuremath{\nu}=1/3$, $\ensuremath{\nu}=1/5$, and $\ensuremath{\nu}=5/2$. The results for $\ensuremath{\nu}=1/3$ and $\ensuremath{\nu}=1/5$ are consistent with the topological entanglement entropy for the Laughlin wave function. The $\ensuremath{\nu}=5/2$ state exhibits a topological entanglement entropy consistent with the Moore-Read wave function.

DOI
10.1103/physrevb.78.035320

Related papers

TOPOLOGICAL ENTANGLEMENT ENTROPY IN THE SECOND LANDAU LEVEL

Barry Friedman, Gregory Levine

The entanglement entropy of the incompressible states of a realistic quantum Hall system in the second Landau level is studied by direct diagonalization. The subdominant term of the area law, the topological entanglement entropy, which is believed to carry information about topological order in the ground state, was extracted for filling factors ν = 12/5 and ν = 7/3. While it is difficult to make strong conclusions about ν = 12/5, the ν = 7/3 state appears to be very consistent with the topological entanglement entropy for the k = 4 Read–Rezayi state. The effect of finite thickness corrections to the Coulomb potential used in the direct diagonalization is also systematically studied.

arXiv:0902.1524•International Journal of Modern Physics B•Sep 30, 2010•7 citations

Entanglement measures for quasi-two-dimensional fractional quantum Hall states

John Biddle, Michael R. Peterson, S. Das Sarma

We theoretically examine entanglement in fractional quantum hall states, explicitly taking into account and emphasizing the quasi-two-dimensional nature of experimental quantum Hall systems. In particular, we study the entanglement entropy and the entanglement spectrum as a function of the finite layer thickness, $d$, of the quasi-two-dimensional system for a number of filling fractions $\ensuremath{\nu}$ in the lowest and the second Landau levels: $\ensuremath{\nu}$ = 1/3, 7/3, 1/2, and 5/2. We observe that the entanglement measures are dependent on which Landau level the electrons fractionally occupy, and find that filling fractions 1/3 and 7/3, which are considered to be Laughlin states, weaken with $d$ in the lowest Landau level ($\ensuremath{\nu}=1/3$) and strengthen with $d$ in the second Landau level ($\ensuremath{\nu}=7/3$). For the enigmatic even-denominator $\ensuremath{\nu}=5/2$ state, we find that entanglement in the ground state is consistent with that of the non-Abelian Moore-Read Pfaffian state at an optimal thickness, $d$. We also find that the single-layer $\ensuremath{\nu}=1/2$ system is not a fractional quantum Hall state consistent with the experimental observation. In general, our theoretical findings based on entanglement considerations are completely consistent with the results based on wave-function overlap calculations.

arXiv:1105.1385•Physical Review B•Sep 30, 2011•15 citations

Bipartite entanglement entropy in fractional quantum Hall states

O. S. Zozulya, Masudul Haque, Kareljan Schoutens +1 more

We present a detailed analysis of bipartite entanglement entropies in fractional quantum Hall (FQH) states, considering both Abelian (Laughlin) and non-Abelian (Moore-Read) states. We derive upper bounds for the entanglement between two subsets of the particles making up the state. We also consider the entanglement between spatial regions supporting a FQH state. Using the latter, we show how the so-called topological entanglement entropy $\ensuremath{\gamma}$ of a FQH state can be extracted from wave functions for a limited number of particles.

arXiv:0705.4176•Physical Review B•Sep 18, 2007•127 citations

Entanglement entropy of integer quantum Hall states

Ivan Dario Jimenez Rodriguez, Germán Sierra

We compute the entanglement entropy, in the real space, of the ground state of the integer Quantum Hall states for three different domains embedded in the cylinder, the disk and the sphere. We establish the validity of the area law with a vanishing value of the topological entanglement entropy. The entropy per unit length of the perimeter depends on the filling fraction, but it is independent of the geometry.

arXiv:0811.2188•Physical Review B•Oct 7, 2009•70 citations

Topological properties of the FQH quasiparticles from the entanglement entropy

Na Jiang, Zi-Xiang Hu

The topological entanglement entropy is a robust measurement of the quantum many-body state with topological order. In fractional quantum Hall (FQH) state, it has a connection to the quantum dimension of the state itself and its quasihole excitations from the conformal field theory (CFT) description. We systematically study the entanglement entropy in the Laughlin, Moore-Read, and Read-Rezayi FQH states. The Abelian nature of the quasihole manifests in the invariant of the entanglement entropy and spectrum while it is created in the subsystem. Whereas the non-Abelian quasihole excitation induces an extra correction of the topological entanglement entropy and the changing of the structure of the entanglement spectrum. The quantum dimension of the quasihole can be obtained from the entropy difference before and after inserting the quasihole. On the other hand, the entanglement entropy behaviors similarly to the density profile and has less oscillations far away from the center of quasihole. It gives us a better definition of the quasihole boundary and the measurement of the size of the quasihole.

•Nov 3, 2015•0 citations

Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States

Hui Li, F. D. M. Haldane

We study the "entanglement spectrum" (a presentation of the Schmidt decomposition analogous to a set of "energy levels") of a many-body state, and compare the Moore-Read model wave function for the nu=5/2 fractional quantum Hall state with a generic 5/2 state obtained by finite-size diagonalization of the second-Landau-level-projected Coulomb interactions. Their spectra share a common "gapless" structure, related to conformal field theory. In the model state, these are the only levels, while in the "generic" case, they are separated from the rest of the spectrum by a clear "entanglement gap", which appears to remain finite in the thermodynamic limit. We propose that the low-lying entanglement spectrum can be used as a "fingerprint" to identify topological order.

arXiv:0805.0332•Physical Review Letters•Jul 3, 2008•1,647 citations
The entanglement entropy of the incompressible states of a realistic quantum Hall system is studied by direct diagonalization. The subdominant term to the area law, the topological entanglement entropy (which is believed to carry information about topologic order in the ground state), was extracted for filling factors \ensuremathν=1/3\ensuremath{\nu}=1/3\ensuremathν=1/3, \ensuremathν=1/5\ensuremath{\nu}=1/5\ensuremathν=1/5, and \ensuremathν=5/2\ensuremath{\nu}=5/2\ensuremathν=5/2. The results for \ensuremathν=1/3\ensuremath{\nu}=1/3\ensuremathν=1/3 and \ensuremathν=1/5\ensuremath{\nu}=1/5\ensuremathν=1/5 are consistent with the topological entanglement entropy for the Laughlin wave function. The \ensuremathν=5/2\ensuremath{\nu}=5/2\ensuremathν=5/2 state exhibits a topological entanglement entropy consistent with the Moore-Read wave function.
The entanglement entropy of the incompressible states of a realistic quantum Hall system in the second Landau level is studied by direct diagonalization. The subdominant term of the area law, the topological entanglement entropy, which is believed to carry information about topological order in the ground state, was extracted for filling factors ν = 12/5 and ν = 7/3. While it is difficult to make strong conclusions about ν = 12/5, the ν = 7/3 state appears to be very consistent with the topological entanglement entropy for the k = 4 Read–Rezayi state. The effect of finite thickness corrections to the Coulomb potential used in the direct diagonalization is also systematically studied.
We theoretically examine entanglement in fractional quantum hall states, explicitly taking into account and emphasizing the quasi-two-dimensional nature of experimental quantum Hall systems. In particular, we study the entanglement entropy and the entanglement spectrum as a function of the finite layer thickness, ddd, of the quasi-two-dimensional system for a number of filling fractions $\ensuremath{\nu}$ in the lowest and the second Landau levels: $\ensuremath{\nu}$ = 1/3, 7/3, 1/2, and 5/2. We observe that the entanglement measures are dependent on which Landau level the electrons fractionally occupy, and find that filling fractions 1/3 and 7/3, which are considered to be Laughlin states, weaken with ddd in the lowest Landau level ($\ensuremath{\nu}=1/3$) and strengthen with ddd in the second Landau level ($\ensuremath{\nu}=7/3$). For the enigmatic even-denominator $\ensuremath{\nu}=5/2$ state, we find that entanglement in the ground state is consistent with that of the non-Abelian Moore-Read Pfaffian state at an optimal thickness, ddd. We also find that the single-layer $\ensuremath{\nu}=1/2$ system is not a fractional quantum Hall state consistent with the experimental observation. In general, our theoretical findings based on entanglement considerations are completely consistent with the results based on wave-function overlap calculations.
We present a detailed analysis of bipartite entanglement entropies in fractional quantum Hall (FQH) states, considering both Abelian (Laughlin) and non-Abelian (Moore-Read) states. We derive upper bounds for the entanglement between two subsets of the particles making up the state. We also consider the entanglement between spatial regions supporting a FQH state. Using the latter, we show how the so-called topological entanglement entropy $\ensuremath{\gamma}$ of a FQH state can be extracted from wave functions for a limited number of particles.
The topological entanglement entropy is a robust measurement of the quantum many-body state with topological order. In fractional quantum Hall (FQH) state, it has a connection to the quantum dimension of the state itself and its quasihole excitations from the conformal field theory (CFT) description. We systematically study the entanglement entropy in the Laughlin, Moore-Read, and Read-Rezayi FQH states. The Abelian nature of the quasihole manifests in the invariant of the entanglement entropy and spectrum while it is created in the subsystem. Whereas the non-Abelian quasihole excitation induces an extra correction of the topological entanglement entropy and the changing of the structure of the entanglement spectrum. The quantum dimension of the quasihole can be obtained from the entropy difference before and after inserting the quasihole. On the other hand, the entanglement entropy behaviors similarly to the density profile and has less oscillations far away from the center of quasihole. It gives us a better definition of the quasihole boundary and the measurement of the size of the quasihole.
We study the "entanglement spectrum" (a presentation of the Schmidt decomposition analogous to a set of "energy levels") of a many-body state, and compare the Moore-Read model wave function for the nu=5/2 fractional quantum Hall state with a generic 5/2 state obtained by finite-size diagonalization of the second-Landau-level-projected Coulomb interactions. Their spectra share a common "gapless" structure, related to conformal field theory. In the model state, these are the only levels, while in the "generic" case, they are separated from the rest of the spectrum by a clear "entanglement gap", which appears to remain finite in the thermodynamic limit. We propose that the low-lying entanglement spectrum can be used as a "fingerprint" to identify topological order.