arXiv subjects

V. Terras

Publications and source records attributed to V. Terras.

41 records · Page 3Linked to original sources

arXiv1999

On the quantum inverse scattering problem

A general method for solving the so-called quantum inverse scattering problem (namely the reconstruction of local quantum (field) operators in term of the quantum monodromy matrix satisfying a Yang-Baxter quadratic algebra governed by an R-matrix) for a large class of lattice quantum integrable models is given. The principal requirement being the initial condition (R(0) = P, the permutation operator) for the quantum R-matrix solving the Yang-Baxter equation, it applies not only to most known integrable fundamental lattice models (such as Heisenberg spin chains) but also to lattice models with arbitrary number of impurities and to the so-called fused lattice models (including integrable higher spin generalizations of Heisenberg chains). Our method is then applied to several important examples like the sl(n) XXZ model, the XYZ spin-1/2 chain and also to the spin-s Heisenberg chains.

hep-th↗

arXiv1999

Correlation functions of the XXZ Heisenberg spin-1/2 chain in a magnetic field

Using the algebraic Bethe ansatz method, and the solution of the quantum inverse scattering problem for local spins, we obtain multiple integral representations of the $n$-point correlation functions of the XXZ Heisenberg spin-$1 \over 2$ chain in a constant magnetic field. For zero magnetic field, this result agrees, in both the massless and massive (anti-ferromagnetic) regimes, with the one obtained from the q-deformed KZ equations (massless regime) and the representation theory of the quantum affine algebra ${\cal U}_q (\hat{sl}_2)$ together with the corner transfer matrix approach (massive regime).

math-ph↗

arXiv1999

Drinfel'd Twists and Functional Bethe Ansatz

Using Functional Bethe Ansatz technique, factorizing Drinfel'd Twists for any finite dimensional irreducible representations of the Yangian Y(sl(2)) are constructed.

math-ph↗

arXiv1998

Spontaneous magnetization of the XXZ Heisenberg spin-1/2 chain

Determinant representations of form factors are used to represent the spontaneous magnetization of the Heisenberg XXZ chain (Delta >1) on the finite lattice as the ratio of two determinants. In the thermodynamic limit (the lattice of infinite length), the Baxter formula is reproduced in the framework of Algebraic Bethe Ansatz. It is shown that the finite size corrections to the Baxter formula are exponentially small.

solv-int↗

arXiv1998

Form factors of the XXZ Heisenberg spin-1/2 finite chain

Form factors for local spin operators of the XXZ Heisenberg spin-1/2 finite chain are computed. Representation theory of Drinfel'd twists for the sl2 quantum affine algebra in finite dimensional modules is used to calculate scalar products of Bethe states (leading to Gaudin formula) and to solve the quantum inverse problem for local spin operators in the finite XXZ chain. Hence, we obtain the representation of the n-spin correlation functions in terms of expectation values(in ferromagnetic reference state) of the operator entries of the quantum monodromy matrix satisfying Yang-Baxter algebra. This leads to the direct calculation of the form factors of the XXZ Heisenberg spin-1/2 finite chain as determinants of usual functions of the parameters of the model. A two-point correlation function for adjacent sites is also derived using similar techniques.

math-ph↗