11th Bologna Workshop on Conformal Field Theory and Integrable Models

Applications of the Modified Algebraic Bethe Ansatz (MABA): Rectangular 6-Vertex Model with General Boundary Conditions (r6V-GBC) and Full Counting Statistics (FCS) for the XXX Twisted Spin Chain

4 Sept 2025, 15:10

25m

Aula Magna (Dept. of Physics and Astronomy - University of Bologna)

Talk (25 min) Talks

Speaker

Samuel Belliard (IDP Tours France)

Description

We present recent applications of the Modified Algebraic Bethe Ansatz (MABA) to two-dimensional vertex models and one-dimensional spin chains.

First, we address the eigenvalue problem and scalar products within the MABA framework. In particular, we exploit the SL₂ invariance of the underlying R-matrix and introduce a modified representation theory that generalizes the conventional highest-weight formalism.

Next, we study the rectangular 6-vertex model with general boundary conditions (r6V-GBC), characterized by modified creation operators in the MABA and pseudo vectors from modified representation theory. We analyze both the homogeneous and thermodynamic limits, deriving boundary effects on the leading term of the free energy.

Finally, by applying the MABA to two distinct twists and using modified Slavnov scalar products, we obtain the Full Counting Statistics (FCS) for the XXX twisted spin chain.

This work was conducted in collaboration with R. Pimenta, N. Slavnov, B. Vallet, M. Cornillault and A. Hutsalyuk.

Presentation materials

Talk Bologne 2025.pdf