An alternative method for extracting the von Neumann entropy from Rényi entropies
Abstract An alternative method is presented for extracting the von Neumann entropy − Tr(ρ ln ρ) from Tr(ρ n ) for integer n in a quantum system with density matrix ρ. Instead of relying on direct analytic continuation in n, the method uses a generating function − Tr{ρ ln[(1 − zρ)/(1 − z)]} of an aux...
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Online Access: | https://doi.org/10.1007/JHEP01(2021)042 |
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doaj-4bdb5e4dbf1a473cb4f6fbf7ccb51c522021-01-17T12:07:09ZengSpringerOpenJournal of High Energy Physics1029-84792021-01-012021112310.1007/JHEP01(2021)042An alternative method for extracting the von Neumann entropy from Rényi entropiesEric D’Hoker0Xi Dong1Chih-Hung Wu2Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy, University of CaliforniaDepartment of Physics, University of CaliforniaDepartment of Physics, University of CaliforniaAbstract An alternative method is presented for extracting the von Neumann entropy − Tr(ρ ln ρ) from Tr(ρ n ) for integer n in a quantum system with density matrix ρ. Instead of relying on direct analytic continuation in n, the method uses a generating function − Tr{ρ ln[(1 − zρ)/(1 − z)]} of an auxiliary complex variable z. The generating function has a Taylor series that is absolutely convergent within |z| < 1, and may be analytically continued in z to z = −∞ where it gives the von Neumann entropy. As an example, we use the method to calculate analytically the CFT entanglement entropy of two intervals in the small cross ratio limit, reproducing a result that Calabrese et al. obtained by direct analytic continuation in n. Further examples are provided by numerical calculations of the entanglement entropy of two intervals for general cross ratios, and of one interval at finite temperature and finite interval length.https://doi.org/10.1007/JHEP01(2021)042Conformal Field TheoryField Theories in Lower Dimensions |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Eric D’Hoker Xi Dong Chih-Hung Wu |
spellingShingle |
Eric D’Hoker Xi Dong Chih-Hung Wu An alternative method for extracting the von Neumann entropy from Rényi entropies Journal of High Energy Physics Conformal Field Theory Field Theories in Lower Dimensions |
author_facet |
Eric D’Hoker Xi Dong Chih-Hung Wu |
author_sort |
Eric D’Hoker |
title |
An alternative method for extracting the von Neumann entropy from Rényi entropies |
title_short |
An alternative method for extracting the von Neumann entropy from Rényi entropies |
title_full |
An alternative method for extracting the von Neumann entropy from Rényi entropies |
title_fullStr |
An alternative method for extracting the von Neumann entropy from Rényi entropies |
title_full_unstemmed |
An alternative method for extracting the von Neumann entropy from Rényi entropies |
title_sort |
alternative method for extracting the von neumann entropy from rényi entropies |
publisher |
SpringerOpen |
series |
Journal of High Energy Physics |
issn |
1029-8479 |
publishDate |
2021-01-01 |
description |
Abstract An alternative method is presented for extracting the von Neumann entropy − Tr(ρ ln ρ) from Tr(ρ n ) for integer n in a quantum system with density matrix ρ. Instead of relying on direct analytic continuation in n, the method uses a generating function − Tr{ρ ln[(1 − zρ)/(1 − z)]} of an auxiliary complex variable z. The generating function has a Taylor series that is absolutely convergent within |z| < 1, and may be analytically continued in z to z = −∞ where it gives the von Neumann entropy. As an example, we use the method to calculate analytically the CFT entanglement entropy of two intervals in the small cross ratio limit, reproducing a result that Calabrese et al. obtained by direct analytic continuation in n. Further examples are provided by numerical calculations of the entanglement entropy of two intervals for general cross ratios, and of one interval at finite temperature and finite interval length. |
topic |
Conformal Field Theory Field Theories in Lower Dimensions |
url |
https://doi.org/10.1007/JHEP01(2021)042 |
work_keys_str_mv |
AT ericdhoker analternativemethodforextractingthevonneumannentropyfromrenyientropies AT xidong analternativemethodforextractingthevonneumannentropyfromrenyientropies AT chihhungwu analternativemethodforextractingthevonneumannentropyfromrenyientropies AT ericdhoker alternativemethodforextractingthevonneumannentropyfromrenyientropies AT xidong alternativemethodforextractingthevonneumannentropyfromrenyientropies AT chihhungwu alternativemethodforextractingthevonneumannentropyfromrenyientropies |
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