A distribution approach to finite-size corrections in Bethe Ansatz solvable models
We present a new and efficient method for deriving finite-size effects in statistical physics models solvable by Bethe Ansatz. It is based on the study of the functional that maps a function to the sum of its evaluations over the Bethe roots. A simple and powerful constraint is derived when applying...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2018-09-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321318301585 |
| _version_ | 1818454218937204736 |
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| author | Etienne Granet Jesper Lykke Jacobsen Hubert Saleur |
| author_facet | Etienne Granet Jesper Lykke Jacobsen Hubert Saleur |
| author_sort | Etienne Granet |
| collection | DOAJ |
| description | We present a new and efficient method for deriving finite-size effects in statistical physics models solvable by Bethe Ansatz. It is based on the study of the functional that maps a function to the sum of its evaluations over the Bethe roots. A simple and powerful constraint is derived when applying this functional to infinitely derivable test functions with compact support, that generalizes then to more general test functions.The method is presented in the context of the simple spin-1/2 XXZ chain for which we derive the finite-size corrections to leading eigenvalues of the Hamiltonian for any configuration of Bethe numbers with real Bethe roots. The expected results for the central charge and conformal dimensions are recovered. |
| first_indexed | 2024-12-14T21:51:24Z |
| format | Article |
| id | doaj.art-826774b98cbf4dc6bc100a1d6924173e |
| institution | Directory Open Access Journal |
| issn | 0550-3213 |
| language | English |
| last_indexed | 2024-12-14T21:51:24Z |
| publishDate | 2018-09-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj.art-826774b98cbf4dc6bc100a1d6924173e2022-12-21T22:46:14ZengElsevierNuclear Physics B0550-32132018-09-0193496117A distribution approach to finite-size corrections in Bethe Ansatz solvable modelsEtienne Granet0Jesper Lykke Jacobsen1Hubert Saleur2Institut de Physique Théorique, CEA Saclay, 91191 Gif-sur-Yvette, France; Laboratoire de physique théorique, Département de physique de l'ENS, École Normale Supérieure, UPMC Univ. Paris 06, CNRS, PSL Research University, 75005 Paris, France; Corresponding author.Institut de Physique Théorique, CEA Saclay, 91191 Gif-sur-Yvette, France; Laboratoire de physique théorique, Département de physique de l'ENS, École Normale Supérieure, UPMC Univ. Paris 06, CNRS, PSL Research University, 75005 Paris, France; Sorbonne Universités, UPMC Univ. Paris 06, École Normale Supérieure, CNRS, Laboratoire de Physique Théorique (LPT ENS), 75005 Paris, FranceInstitut de Physique Théorique, CEA Saclay, 91191 Gif-sur-Yvette, France; USC Physics Department, Los Angeles CA 90089, USAWe present a new and efficient method for deriving finite-size effects in statistical physics models solvable by Bethe Ansatz. It is based on the study of the functional that maps a function to the sum of its evaluations over the Bethe roots. A simple and powerful constraint is derived when applying this functional to infinitely derivable test functions with compact support, that generalizes then to more general test functions.The method is presented in the context of the simple spin-1/2 XXZ chain for which we derive the finite-size corrections to leading eigenvalues of the Hamiltonian for any configuration of Bethe numbers with real Bethe roots. The expected results for the central charge and conformal dimensions are recovered.http://www.sciencedirect.com/science/article/pii/S0550321318301585 |
| spellingShingle | Etienne Granet Jesper Lykke Jacobsen Hubert Saleur A distribution approach to finite-size corrections in Bethe Ansatz solvable models Nuclear Physics B |
| title | A distribution approach to finite-size corrections in Bethe Ansatz solvable models |
| title_full | A distribution approach to finite-size corrections in Bethe Ansatz solvable models |
| title_fullStr | A distribution approach to finite-size corrections in Bethe Ansatz solvable models |
| title_full_unstemmed | A distribution approach to finite-size corrections in Bethe Ansatz solvable models |
| title_short | A distribution approach to finite-size corrections in Bethe Ansatz solvable models |
| title_sort | distribution approach to finite size corrections in bethe ansatz solvable models |
| url | http://www.sciencedirect.com/science/article/pii/S0550321318301585 |
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