Berlin 2018 – scientific programme

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TT: Fachverband Tiefe Temperaturen

TT 36: Correlated Electrons: 1D Theory

TT 36.7: Talk

Tuesday, March 13, 2018, 11:15–11:30, HFT-FT 101

Systematic reduction of Thermodynamic Bethe Ansatz equations by means of Bäcklund hierarchies — •Eyzo Stouten and Andreas Klümper — Bergische Universität Wuppertal, 42097 Wuppertal, Germany

For integrable systems there is an established way to calculate thermodynamics through the Thermodynamic Bethe Ansatz. The conventional method necessarily involves the characterization of the full spectrum of the Hamiltonian via combinatorial means. An alternative approach is to study the leading eigenvalue of a column to column or quantum transfer matrix (QTM), which is related to an infinite family of QTM by factorization of the bilinear fusion relations (of Hirota type). By studying the analyticity of the constituents of the QTM one can rewrite the fusion relations into non-linear integral equations (NLIE) that characterize the leading eigenvalue. This transformation only depends on some knowledge of the partial spectrum of the QTM.

To extract the thermodynamic properties at finite temperatures the infinite hierarchy of NLIE is truncated to a finite set at the cost of introducing a finite set of auxiliary equations. In previous works these auxiliary equations could only be derived in a heuristic manner for low rank systems. The goal of this research is to derive them in a systematic way by factorization of a set of bilinear Bäcklund equations and extending to arbitrary rank. The use of Bäcklund relations is inspired by a series of papers [1] where they where introduced because of their relation to the Hirota equations and the related fusion relations.
Zabrodin et al., Nucl. Phys. B 790 (2008) 345