On exact overlaps for gl(N) symmetric spin chains
We study the integrable two-site states of the quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing gl(N)-invariant R-matrix. We investigate the overlaps between the integrable two-site states and the wave-functions. To find exact derivations for the factorized over...
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| Format: | Article |
| Language: | English |
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Elsevier
2022-10-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321322002607 |
| _version_ | 1811274975020056576 |
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| author | Tamás Gombor |
| author_facet | Tamás Gombor |
| author_sort | Tamás Gombor |
| collection | DOAJ |
| description | We study the integrable two-site states of the quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing gl(N)-invariant R-matrix. We investigate the overlaps between the integrable two-site states and the wave-functions. To find exact derivations for the factorized overlap formulas for the nested integrable systems is a longstanding unsolved problem. In this paper we give a derivation for a large class of the integrable states of the gl(N) symmetric spin chain. The first part of the derivation is to calculate recurrence relations for the off-shell overlap that uniquely fix it. Using these recursions we prove that the normalized overlaps of the multi-particle states have factorized forms which contain the products of the one-particle overlaps and the ratio of the Gaudin-like determinants. We also show that the previously proposed overlap formulas agree with our general formula. |
| first_indexed | 2024-04-12T23:29:53Z |
| format | Article |
| id | doaj.art-d29cc85c9edc4acab2ca81dfbbecec42 |
| institution | Directory Open Access Journal |
| issn | 0550-3213 |
| language | English |
| last_indexed | 2024-04-12T23:29:53Z |
| publishDate | 2022-10-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj.art-d29cc85c9edc4acab2ca81dfbbecec422022-12-22T03:12:19ZengElsevierNuclear Physics B0550-32132022-10-01983115909On exact overlaps for gl(N) symmetric spin chainsTamás Gombor0MTA-ELTE “Momentum” Integrable Quantum Dynamics Research Group, Department of Theoretical Physics, Eötvös Loránd University, Holographic QFT Group, Wigner Research Centre for Physics, Budapest, HungaryWe study the integrable two-site states of the quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing gl(N)-invariant R-matrix. We investigate the overlaps between the integrable two-site states and the wave-functions. To find exact derivations for the factorized overlap formulas for the nested integrable systems is a longstanding unsolved problem. In this paper we give a derivation for a large class of the integrable states of the gl(N) symmetric spin chain. The first part of the derivation is to calculate recurrence relations for the off-shell overlap that uniquely fix it. Using these recursions we prove that the normalized overlaps of the multi-particle states have factorized forms which contain the products of the one-particle overlaps and the ratio of the Gaudin-like determinants. We also show that the previously proposed overlap formulas agree with our general formula.http://www.sciencedirect.com/science/article/pii/S0550321322002607 |
| spellingShingle | Tamás Gombor On exact overlaps for gl(N) symmetric spin chains Nuclear Physics B |
| title | On exact overlaps for gl(N) symmetric spin chains |
| title_full | On exact overlaps for gl(N) symmetric spin chains |
| title_fullStr | On exact overlaps for gl(N) symmetric spin chains |
| title_full_unstemmed | On exact overlaps for gl(N) symmetric spin chains |
| title_short | On exact overlaps for gl(N) symmetric spin chains |
| title_sort | on exact overlaps for gl n symmetric spin chains |
| url | http://www.sciencedirect.com/science/article/pii/S0550321322002607 |
| work_keys_str_mv | AT tamasgombor onexactoverlapsforglnsymmetricspinchains |