Form Factor Approach to the Calculation of Correlation Functions of Integrable Models

B. L. Altshuler, Robert Konik, Alexei M. Tsvelik

Giuseppe Mussardo

Frank Göhmann, Michael Karbach, Andreas Klümper +2 more

Abstract We propose a method for calculating dynamical correlation functions at finite temperature in integrable lattice models of Yang–Baxter type. The method is based on an expansion of the correlation functions as a series over matrix elements of a time-dependent quantum transfer matrix rather than the Hamiltonian. In the infinite Trotter-number limit the matrix elements become time independent and turn into the thermal form factors studied previously in the context of static correlation functions. We make this explicit with the example of the XXZ model. We show how the form factors can be summed utilizing certain auxiliary functions solving finite sets of nonlinear integral equations. The case of the XX model is worked out in more detail leading to a novel form-factor series representation of the dynamical transverse two-point function.

V. E. Korepin, N. A. Slavnov

We consider the quantum sinh-Gordon model in this paper. Form factors in this model were calculated by Mussardo and colleagues. We sum up all contributions of form factors and obtain a closed expression for a correlation function. This expression is a determinant of an integral operator. Similar determinant representations have been proven to be useful not only in the theory of correlation functions, but also in matrix models.

均 今野

S. Belliard, S Pakuliak, E. Ragoucy +1 more

We study SU(3)-invariant integrable models solvable by nested algebraic Bethe ansatz. We obtain determinant representations for form factors of diagonal entries of the monodromy matrix. This representation can be used for the calculation of form factors and correlation functions of the XXX SU(3)-invariant Heisenberg chain.