Functional Integral Approach to Some Models of Solid State Physics

Nguyễn Văn Hiếu

D Levy-Bencheton, V. Terras

We consider the problem of the exact computation of the correlation functions of the eight-vertex solid-on-solid model by means of the algebraic Bethe ansatz. We compute the scalar product between a Bethe eigenstate and an arbitrary state of Bethe type and show that, in the cyclic case, it can be formulated as a single determinant of usual functions. It allows us to obtain determinant representations for finite-size form factors. By summing up over the form factors, we also give a multiple-integral representation for a generating function of the two-point function.

Daniel Westerfeld, Maxime Großpietsch, Hannes Kakuschke +1 more

Abstract We study reduced density matrices of the integrable critical restricted solid-on-solid (RSOS) model in a particular topological sector containing the ground state. Similar as in the spin- 1 / 2 Heisenberg model it has been observed that correlation functions of this model on short segments can be ‘factorized’: they are completely determined by a single nearest-neighbour two-point function ω and a set of structure functions. While ω captures the dependence on the system size and the state of the system the structure functions can be expressed in terms of the possible operators on the segment, in the present case representations of the Temperley–Lieb algebra TL n , and are independent of the model parameters. We present explicit results for the function ω in the infinite system ground state of the model and compute multi-point local height probabilities for up to four adjacent sites for the RSOS model and the related three-point correlation functions of non-Abelian s u ( 2 ) k anyons.