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Veranstaltungskalender der Bergischen Universität Wuppertal

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Student Workshop on Integrability, March 23 - 26, 2020

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Kategorie: Kolloquium
Termin Kategorie Veranstaltung Ort
Di24Mär
10:30 Uhr -
11:30 Uhr
Kategorie: Kolloquium

Student Workshop on Integrability, March 23 - 26, 2020

Prof. Dr. Andreas Klümper, Bergische Universität Wuppertal

Campus Grifflenberg, Hörsaal 8 (Gebäude G, Ebene 10, Raum 03), Gaußstr. 20

Student Workshop on Integrability, March 23 - 26, 2020

Org. Univ.-Prof. Dr. Andreas Klümper / M. Sc. Philipp Jaeger, Fk.04 - Mathematik und Naturwissenschaften, AG Theoretische Physik

Thermodynamics and finite-size studies of integrable models: From TBA equations to reduced non-linear integral equations

In this talk I will present a unified treatment for the calculation of finite-size data to the energy eigenvalues of integrable Hamiltonians and of their thermodynamic potentials at arbitrary temperatures. The goal is achieved in two steps. First a Trotter-Suzuki like mapping of the Hamiltonian to an exactly solvable staggered vertex model and the formulation of a suitable transfer direction reduces the problem of thermodynamics to the calculation of just the leading eigenvalue of the quantum transfer matrix. This task is very much like that for calculating eigenvalues for finite row-to-row transfer matrices of integrable vertex models. The second step concerns the actual calculation of the eigenvalues either by use of a Bethe ansatz or by use of the fusion procedure and solving functional equations of T- and Y-system type.

This will result in coupled non-linear integral equations (NLIE) of thermodynamical Bethe ansatz (TBA) type. I will show how in general, without restricting the treatment to special anisotropies corresponding to roots of unity and without approximation errors, the NLIEs can be truncated to a finite set. The seminal models for the presentation of these methods will be su(2) invariant systems. However, some generalizations to higher rank models will be given.

https://integrability.pj4e.de/program-2020/