From Bäcklund transforms to finite sets of non-linear integral equations : study and application of new techniques in thermodynamic Bethe Ansatz / vorgelegt von Eyzo Stouten. Wuppertal, 30th June 2024
Inhalt
- Introduction
- Quantum transfer matrix
- Row-to-row transfer matrix and fundamental relations
- Quantum Transfer Matrix & partition function
- Explicit expressions for the QTM
- Properties of the QTM
- Fusion
- Fusion hierarchy
- Normalization
- Asymptotic value of Tas(u), connection to Schur character formula
- Pictorial method for fusion equations
- Analyticity conditions of fused QTM eigenvalues
- From functional relations to non-linear integral equations
- Bäcklund Formalism
- Hirota equation in classical and quantum integrability
- Bäcklund transform and ALP
- Conjugate set of ALP for QTM
- Combined formulation of the boundary conditions
- Eigenvalues of the Bäcklund functions for Uq[SU(3)]
- Pictorial method for Bäcklund equations
- Results for SU(3) symmetric QTM
- The Auxiliary functions Uq[SU(3)]
- Derivation of the NLIE
- QTM eigenvalue & asymptotic behavior
- Numerical evaluation
- Low temperature asymptotics
- Bäcklund formalism for Uq[SU(n)] symmetric models
- The Uq[SU(4)] case
- Auxiliary linear problems and boundary conditions for Uq[SU(n)]
- Pictorial approach for Uq[SU(4)]
- Unknown functions in the pictorial approach
- Pictorial approach solution for SU(4) and comparison to known solution
- Conclusion
- List of publications
- Appendices
- Fusion
- Nested Bethe ansatz for the QTM in Uq[SU(3)]
- First embedding scheme B(u)=(B1(u),B2(u))
- Second embedding scheme B(u)=(B1(u),B2(u))T
- Yang-Baxter Algebra and Bethe vectors of different embeddings
- Auxiliary functions in previous works
- Details of the NLIE derivation for SU(3)
- Acknowledgments