Edge state inner products and real-space entanglement spectrum of trial quantum Hall states
We consider the trial wavefunctions for the Fractional Quantum Hall Effect (FQHE) that are given by conformal blocks, and construct their associated edge excited states in full generality. The inner products between these edge states are computed in the thermodynamic limit, assuming generalized scre...
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ftdatacite:10.48550/arxiv.1207.7119 2023-05-15T16:55:52+02:00 Edge state inner products and real-space entanglement spectrum of trial quantum Hall states Dubail, J. Read, N. Rezayi, E. H. 2012 https://dx.doi.org/10.48550/arxiv.1207.7119 https://arxiv.org/abs/1207.7119 unknown arXiv https://dx.doi.org/10.1103/physrevb.86.245310 arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ Mesoscale and Nanoscale Physics cond-mat.mes-hall Strongly Correlated Electrons cond-mat.str-el High Energy Physics - Theory hep-th Quantum Physics quant-ph FOS Physical sciences article-journal Article ScholarlyArticle Text 2012 ftdatacite https://doi.org/10.48550/arxiv.1207.7119 https://doi.org/10.1103/physrevb.86.245310 2022-04-01T13:42:52Z We consider the trial wavefunctions for the Fractional Quantum Hall Effect (FQHE) that are given by conformal blocks, and construct their associated edge excited states in full generality. The inner products between these edge states are computed in the thermodynamic limit, assuming generalized screening (i.e. short-range correlations only) inside the quantum Hall droplet, and using the language of boundary conformal field theory (boundary CFT). These inner products take universal values in this limit: they are equal to the corresponding inner products in the bulk 2d chiral CFT which underlies the trial wavefunction. This is a bulk/edge correspondence; it shows the equality between equal-time correlators along the edge and the correlators of the bulk CFT up to a Wick rotation. This approach is then used to analyze the entanglement spectrum (ES) of the ground state obtained with a bipartition A\cupB in real-space. Starting from our universal result for inner products in the thermodynamic limit, we tackle corrections to scaling using standard field-theoretic and renormalization group arguments. We prove that generalized screening implies that the entanglement Hamiltonian H_E = - log ρ_A is isospectral to an operator that is local along the cut between A and B. We also show that a similar analysis can be carried out for particle partition. We discuss the close analogy between the formalism of trial wavefunctions given by conformal blocks and Tensor Product States, for which results analogous to ours have appeared recently. Finally, the edge theory and entanglement spectrum of px + ipy paired superfluids are treated in a similar fashion in the appendix. : 32 pages, 6 figures. V2: discussion of corrections to scaling extended, references added Text IPY DataCite Metadata Store (German National Library of Science and Technology) |
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Mesoscale and Nanoscale Physics cond-mat.mes-hall Strongly Correlated Electrons cond-mat.str-el High Energy Physics - Theory hep-th Quantum Physics quant-ph FOS Physical sciences |
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Mesoscale and Nanoscale Physics cond-mat.mes-hall Strongly Correlated Electrons cond-mat.str-el High Energy Physics - Theory hep-th Quantum Physics quant-ph FOS Physical sciences Dubail, J. Read, N. Rezayi, E. H. Edge state inner products and real-space entanglement spectrum of trial quantum Hall states |
topic_facet |
Mesoscale and Nanoscale Physics cond-mat.mes-hall Strongly Correlated Electrons cond-mat.str-el High Energy Physics - Theory hep-th Quantum Physics quant-ph FOS Physical sciences |
description |
We consider the trial wavefunctions for the Fractional Quantum Hall Effect (FQHE) that are given by conformal blocks, and construct their associated edge excited states in full generality. The inner products between these edge states are computed in the thermodynamic limit, assuming generalized screening (i.e. short-range correlations only) inside the quantum Hall droplet, and using the language of boundary conformal field theory (boundary CFT). These inner products take universal values in this limit: they are equal to the corresponding inner products in the bulk 2d chiral CFT which underlies the trial wavefunction. This is a bulk/edge correspondence; it shows the equality between equal-time correlators along the edge and the correlators of the bulk CFT up to a Wick rotation. This approach is then used to analyze the entanglement spectrum (ES) of the ground state obtained with a bipartition A\cupB in real-space. Starting from our universal result for inner products in the thermodynamic limit, we tackle corrections to scaling using standard field-theoretic and renormalization group arguments. We prove that generalized screening implies that the entanglement Hamiltonian H_E = - log ρ_A is isospectral to an operator that is local along the cut between A and B. We also show that a similar analysis can be carried out for particle partition. We discuss the close analogy between the formalism of trial wavefunctions given by conformal blocks and Tensor Product States, for which results analogous to ours have appeared recently. Finally, the edge theory and entanglement spectrum of px + ipy paired superfluids are treated in a similar fashion in the appendix. : 32 pages, 6 figures. V2: discussion of corrections to scaling extended, references added |
format |
Text |
author |
Dubail, J. Read, N. Rezayi, E. H. |
author_facet |
Dubail, J. Read, N. Rezayi, E. H. |
author_sort |
Dubail, J. |
title |
Edge state inner products and real-space entanglement spectrum of trial quantum Hall states |
title_short |
Edge state inner products and real-space entanglement spectrum of trial quantum Hall states |
title_full |
Edge state inner products and real-space entanglement spectrum of trial quantum Hall states |
title_fullStr |
Edge state inner products and real-space entanglement spectrum of trial quantum Hall states |
title_full_unstemmed |
Edge state inner products and real-space entanglement spectrum of trial quantum Hall states |
title_sort |
edge state inner products and real-space entanglement spectrum of trial quantum hall states |
publisher |
arXiv |
publishDate |
2012 |
url |
https://dx.doi.org/10.48550/arxiv.1207.7119 https://arxiv.org/abs/1207.7119 |
genre |
IPY |
genre_facet |
IPY |
op_relation |
https://dx.doi.org/10.1103/physrevb.86.245310 |
op_rights |
arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
op_doi |
https://doi.org/10.48550/arxiv.1207.7119 https://doi.org/10.1103/physrevb.86.245310 |
_version_ |
1766046914717941760 |