On elliptic quantum integrability
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1 On elliptic quantum integrability vertex models, solid-on-solid models and spin chains with Galleas with Galleas thesis Ch I and II thesis Ch I and III in progress with Klabbers thesis Ch IV Jules Lamers PhD advisor Prof. Gleb Arutyunov (DESY)
2 On elliptic quantum integrability vertex models, solid-on-solid models and spin chains with Galleas with Galleas thesis Ch I and II thesis Ch I and III in progress with Klabbers thesis Ch IV Jules Lamers PhD advisor Prof. Gleb Arutyunov (DESY)
3 exactly 'solvable' due to algebraic structure analytic On elliptic quantum integrability vertex models, solid-on-solid models and spin chains with Galleas with Galleas thesis Ch I and II thesis Ch I and III in progress with Klabbers thesis Ch IV Jules Lamers PhD advisor Prof. Gleb Arutyunov (DESY)
4 exactly 'solvable' due to algebraic structure analytic I introduction On elliptic quantum integrability vertex models, solid-on-solid models and spin chains II method with Galleas with Galleas thesis Ch I and II III generalizations thesis Ch I and III IV hopes & dreams in progress with Klabbers thesis Ch IV Jules Lamers PhD advisor Prof. Gleb Arutyunov (DESY)
5 Quantum integrability a brief history Yang-Baxter equation [Baxter '70s] algebra [Faddeev et al '70s] commuting transfer matrices six-vertex model [Sutherland '67] certain models ansatz Heisenberg spin chain [Bethe '31] hidden symmetries [Noether] nice physics; exact results
6 Quantum integrability in general Yang-Baxter equation [Baxter '70s] algebra [Faddeev et al '70s] commuting transfer matrices somesix-vertex model [Sutherland '67] method quantumintegrable models ansatz Heisenberg spin chain [Bethe '31] hidden symmetries [Noether] nice physics; exact results
7 Domain-wall partition function exact computation Uniquely characterized by recursion relation initial condition analytic properties solution found in form of determinant Constructive method algebra: equation for Z at fixed L analysis: relate solutions for successive L [Korepin '82] [Izergin '87] [Galleas ' , JL ' ] solution: symmetrized expression
8 Nice: (meromorphic) solutions are symmetric solutions have special zeroes polynomial solutions: degree fixed [Galleas '12] [Galleas '12, JL '16] [JL '16] Reduction: recursion in L solutions unique (up to normalization) [JL '15] set [JL '16] prescription for constructing Z explicit match with Izergin's determinant solution for to recover Korepin's relation [Galleas '11] [Galleas '11] [JL '16 via Rosengren '09]
9 Elliptic reflecting-end partition function exact computation Uniquely characterized by recursion relation initial condition analytic properties solution found in form of determinant Constructive method algebra: equation for Z at fixed L analysis: relate solutions for successive L [Filali '11] related: [Tsuchiya '95] [Filali Kitanine '10] [Filali '11] [JL '15] related: [Galleas JL '14] solution: symmetrized expression
10 Nice: (meromorphic) solutions are symmetric & crossing symmetric solutions have special zeroes polynomial solutions: degree fixed [JL '15] ~ ~ [JL '15] [JL '15] Reduction: recursion in L solutions unique (up to normalization) [JL '15] set [JL '16] prescription for constructing Z explicit match with Filali's determinant...? solution for to recover Filali's relation ~ ~ [JL '15] [JL '15]
![Partially isotropic Inozemtsev spin chain [Kasteleijn '52] solution: [Orbach '58] [Haldane '88] 'solution': [Haldane et al '92]](/docs-images/87/96338950/images/11-0.jpg "[Inozemtsev '90] solution: [Inozemtsev '92-'00] [Heisenberg '28] solution: [Bethe '31] [Haldane Shastry '88] solution: [Haldane et")
11 Partially isotropic Inozemtsev spin chain [Kasteleijn '52] solution: [Orbach '58] [Haldane '88] 'solution': [Haldane et al '92] [Inozemtsev '90] solution: [Inozemtsev '92-'00] [Heisenberg '28] solution: [Bethe '31] [Haldane Shastry '88] solution: [Haldane et al '92]
12 exactly 'solvable' due to algebraic structure analytic On elliptic quantum integrability vertex models, solid-on-solid models and spin chains with Galleas with Galleas thesis Ch I and II Rick Keesman thesis Ch I and III Prof. Hjalmar Rosengren in progress with Rob Klabbers thesis Ch IV Jules Lamers PhD advisor Prof. Gleb Arutyunov (DESY)
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