Correlation Function and Simplified TBA Equations for XXZ Chain
The calculation of the correlation functions of Bethe ansatz solvable models is very difficult problem. Among these solvable models spin 1/2 XXX chain has been investigated for a long time. Even for this model only the nearest neighbor and the second neighbor correlations were known. In 1990's...
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| Дата: | 2011 |
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| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2011
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146792 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Correlation Function and Simplified TBA Equations for XXZ Chain / M. Takahashi // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 36 назв. — англ. |
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irk-123456789-1467922019-02-12T01:25:08Z Correlation Function and Simplified TBA Equations for XXZ Chain Takahashi, M. The calculation of the correlation functions of Bethe ansatz solvable models is very difficult problem. Among these solvable models spin 1/2 XXX chain has been investigated for a long time. Even for this model only the nearest neighbor and the second neighbor correlations were known. In 1990's multiple integral formula for the general correlations is derived. But the integration of this formula is also very difficult problem. Recently these integrals are decomposed to products of one dimensional integrals and at zero temperature, zero magnetic field and isotropic case, correlation functions are expressed by log 2 and Riemann's zeta functions with odd integer argument ς(3),ς(5),ς(7),.... We can calculate density sub-matrix of successive seven sites. Entanglement entropy of seven sites is calculated. These methods can be extended to XXZ chain up to n=4. Correlation functions are expressed by the generalized zeta functions. Several years ago I derived new thermodynamic Bethe ansatz equation for XXZ chain. This is quite different with Yang-Yang type TBA equations and contains only one unknown function. This equation is very useful to get the high temperature expansion. In this paper we get the analytic solution of this equation at Δ=0. 2011 Article Correlation Function and Simplified TBA Equations for XXZ Chain / M. Takahashi // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 36 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 16T25; 17B37; 82B23 DOI:10.3842/SIGMA.2011.004 http://dspace.nbuv.gov.ua/handle/123456789/146792 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
The calculation of the correlation functions of Bethe ansatz solvable models is very difficult problem. Among these solvable models spin 1/2 XXX chain has been investigated for a long time. Even for this model only the nearest neighbor and the second neighbor correlations were known. In 1990's multiple integral formula for the general correlations is derived. But the integration of this formula is also very difficult problem. Recently these integrals are decomposed to products of one dimensional integrals and at zero temperature, zero magnetic field and isotropic case, correlation functions are expressed by log 2 and Riemann's zeta functions with odd integer argument ς(3),ς(5),ς(7),.... We can calculate density sub-matrix of successive seven sites. Entanglement entropy of seven sites is calculated. These methods can be extended to XXZ chain up to n=4. Correlation functions are expressed by the generalized zeta functions. Several years ago I derived new thermodynamic Bethe ansatz equation for XXZ chain. This is quite different with Yang-Yang type TBA equations and contains only one unknown function. This equation is very useful to get the high temperature expansion. In this paper we get the analytic solution of this equation at Δ=0. |
| format |
Article |
| author |
Takahashi, M. |
| spellingShingle |
Takahashi, M. Correlation Function and Simplified TBA Equations for XXZ Chain Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Takahashi, M. |
| author_sort |
Takahashi, M. |
| title |
Correlation Function and Simplified TBA Equations for XXZ Chain |
| title_short |
Correlation Function and Simplified TBA Equations for XXZ Chain |
| title_full |
Correlation Function and Simplified TBA Equations for XXZ Chain |
| title_fullStr |
Correlation Function and Simplified TBA Equations for XXZ Chain |
| title_full_unstemmed |
Correlation Function and Simplified TBA Equations for XXZ Chain |
| title_sort |
correlation function and simplified tba equations for xxz chain |
| publisher |
Інститут математики НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146792 |
| citation_txt |
Correlation Function and Simplified TBA Equations for XXZ Chain / M. Takahashi // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 36 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:25:40Z |
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