The quantum inverse scattering method and representation theory

Drawing on earlier, seminal works by Bethe and Baxter the Faddeev school developed in the 1980's an approach for obtaining exact solutions in two-dimensional integrable models of statistical mechanics, quantum spin-chains and quantum field theory, known as "quantum inverse scattering method". This method played an essential part in the formulation of quantum groups by Drinfel'd and Jimbo and quantum groups nowadays constitute an active research area within pure mathematics.

Our interest is the application of the representation theory of quantum groups to the aforementioned physical models in order to compute physically relevant quantities such as correlation functions in spin-chains which encode electric, magnetic as well as thermal transport properties of quasi one-dimensional condensed matter systems.

  1. C. Korff, A Q-operator identity for the correlation functions of the infinite XXZ spin-chain, J. Phys. A: Math. Gen. 38 (2005) 6641-6657
  2. C. Korff, Auxiliary matrices on both sides of the equator, J. Phys. A: Math. Gen. 38 (2005) 47-67
  3. C. Korff and I. Roditi, Superalgebras at roots of unity and non-abelian symmetries of integrable models, J. Phys. A: Math. Gen. 35 (2002) 5115-5137
  4. C. Korff and K.A. Seaton, Universal amplitude ratios and Coxeter geometry in the dilute A model, Nucl. Phys. B636 [FS] (2002) 435-464
  5. C. Korff and B.M. McCoy, Loop symmetry of integrable vertex models at roots of unity, Nucl. Phys. B618 (2001) 551-569