On factorized overlaps: Algebraic Bethe Ansatz, twists, and separation of variables
We investigate the exact overlaps between eigenstates of integrable spin chains and a special class of states called “integrable initial/final states”. These states satisfy a special integrability constraint, and they are closely related to integrable boundary conditions. We derive new algebraic rel...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2021-06-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321321000870 |
| _version_ | 1818949883367784448 |
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| author | Tamás Gombor Balázs Pozsgay |
| author_facet | Tamás Gombor Balázs Pozsgay |
| author_sort | Tamás Gombor |
| collection | DOAJ |
| description | We investigate the exact overlaps between eigenstates of integrable spin chains and a special class of states called “integrable initial/final states”. These states satisfy a special integrability constraint, and they are closely related to integrable boundary conditions. We derive new algebraic relations for the integrable states, which lead to a set of recursion relations for the exact overlaps. We solve these recursion relations and thus we derive new overlap formulas, valid in the XXX Heisenberg chain and its integrable higher spin generalizations. Afterwards we generalize the integrability condition to twisted boundary conditions, and derive the corresponding exact overlaps. Finally, we embed the integrable states into the “Separation of Variables” framework, and derive an alternative representation for the exact overlaps of the XXX chain. Our derivations and proofs are rigorous, and they can form the basis of future investigations involving more complicated models such as nested or long-range deformed systems. |
| first_indexed | 2024-12-20T09:09:46Z |
| format | Article |
| id | doaj.art-c392d34be3794b6594eb952b20a5ab47 |
| institution | Directory Open Access Journal |
| issn | 0550-3213 |
| language | English |
| last_indexed | 2024-12-20T09:09:46Z |
| publishDate | 2021-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj.art-c392d34be3794b6594eb952b20a5ab472022-12-21T19:45:36ZengElsevierNuclear Physics B0550-32132021-06-01967115390On factorized overlaps: Algebraic Bethe Ansatz, twists, and separation of variablesTamás Gombor0Balázs Pozsgay1Department of Theoretical Physics and MTA-ELTE “Momentum” Integrable Quantum Dynamics Research Group, Eőtvős Loránd University, Budapest, Hungary; Wigner Research Centre for Physics, Budapest, Hungary; Corresponding author.Department of Theoretical Physics and MTA-ELTE “Momentum” Integrable Quantum Dynamics Research Group, Eőtvős Loránd University, Budapest, HungaryWe investigate the exact overlaps between eigenstates of integrable spin chains and a special class of states called “integrable initial/final states”. These states satisfy a special integrability constraint, and they are closely related to integrable boundary conditions. We derive new algebraic relations for the integrable states, which lead to a set of recursion relations for the exact overlaps. We solve these recursion relations and thus we derive new overlap formulas, valid in the XXX Heisenberg chain and its integrable higher spin generalizations. Afterwards we generalize the integrability condition to twisted boundary conditions, and derive the corresponding exact overlaps. Finally, we embed the integrable states into the “Separation of Variables” framework, and derive an alternative representation for the exact overlaps of the XXX chain. Our derivations and proofs are rigorous, and they can form the basis of future investigations involving more complicated models such as nested or long-range deformed systems.http://www.sciencedirect.com/science/article/pii/S0550321321000870 |
| spellingShingle | Tamás Gombor Balázs Pozsgay On factorized overlaps: Algebraic Bethe Ansatz, twists, and separation of variables Nuclear Physics B |
| title | On factorized overlaps: Algebraic Bethe Ansatz, twists, and separation of variables |
| title_full | On factorized overlaps: Algebraic Bethe Ansatz, twists, and separation of variables |
| title_fullStr | On factorized overlaps: Algebraic Bethe Ansatz, twists, and separation of variables |
| title_full_unstemmed | On factorized overlaps: Algebraic Bethe Ansatz, twists, and separation of variables |
| title_short | On factorized overlaps: Algebraic Bethe Ansatz, twists, and separation of variables |
| title_sort | on factorized overlaps algebraic bethe ansatz twists and separation of variables |
| url | http://www.sciencedirect.com/science/article/pii/S0550321321000870 |
| work_keys_str_mv | AT tamasgombor onfactorizedoverlapsalgebraicbetheansatztwistsandseparationofvariables AT balazspozsgay onfactorizedoverlapsalgebraicbetheansatztwistsandseparationofvariables |