The LeClair-Mussardo series and nested Bethe Ansatz

Abstract

We consider correlation functions in one dimensional quantum integrable models related to the algebra symmetries gl(2|1) and gl(3). Using the algebraic Bethe Ansatz approach we develop an expansion theorem, which leads to an infinite integral series in the thermodynamic limit. The series is the generalization of the LeClair-Mussardo series to nested Bethe Ansatz systems, and it is applicable both to one-point and two-point functions. As an example we consider the ground state density-density correlator in the Gaudin-Yang model of spin-1/2 Fermi particles. Explicit formulas are presented in a special large coupling and large imbalance limit.

Lüscher-corrections for 1-particle form-factors in non-diagonally scattering integrable quantum field theories

“…In the latter case, only the vacuum expectation values have been worked out. Similarly, the LeClair-Mussardo series representation for 2-point functions is known only for some non-relativistic model with gl(3) or gl(2|1) symmetry [37].…”