Abstract
Using U{sub q}SU(2) tensor calculus we compute the two-point scalar operators (TPSO), their averages on the ground-state give the two-point correlation functions. The TPSOs are identified as elements of the Temperley-Lieb algebra and a recurrence relation is given for them. We have not tempted to derive the analytic expressions for the correlation functions in the general case but got some partial results. For q=e{sup i{pi}/3}, all correlation functions are (trivially) zero, for q=e{sup i{pi}/4}, they are related in the continuum to the correlation functions of left-handed and right-handed Majorana fields in the half plane coupled by the boundary condition. In the case q=e{sup i{pi}/6}, one gets the correlation functions of Mittag`s and Stephen`s parafermions for the three-state Potts model. A diagrammatic approach to compute correlation functions is also presented. (orig.)
Hinrichsen, H;
[1]
Martin, P P;
[2]
Rittenberg, V;
[1]
Scheunert, M
[1]
- Bonn Univ. (Germany). Physikalisches Inst.
- City Univ., London (United Kingdom). Dept. of Mathematics
Citation Formats
Hinrichsen, H, Martin, P P, Rittenberg, V, and Scheunert, M.
On the two-point correlation functions for the U{sub q}SU(2)invariant spin one-half Heisenberg chain at roots of unity.
Germany: N. p.,
1993.
Web.
Hinrichsen, H, Martin, P P, Rittenberg, V, & Scheunert, M.
On the two-point correlation functions for the U{sub q}SU(2)invariant spin one-half Heisenberg chain at roots of unity.
Germany.
Hinrichsen, H, Martin, P P, Rittenberg, V, and Scheunert, M.
1993.
"On the two-point correlation functions for the U{sub q}SU(2)invariant spin one-half Heisenberg chain at roots of unity."
Germany.
@misc{etde_10140092,
title = {On the two-point correlation functions for the U{sub q}SU(2)invariant spin one-half Heisenberg chain at roots of unity}
author = {Hinrichsen, H, Martin, P P, Rittenberg, V, and Scheunert, M}
abstractNote = {Using U{sub q}SU(2) tensor calculus we compute the two-point scalar operators (TPSO), their averages on the ground-state give the two-point correlation functions. The TPSOs are identified as elements of the Temperley-Lieb algebra and a recurrence relation is given for them. We have not tempted to derive the analytic expressions for the correlation functions in the general case but got some partial results. For q=e{sup i{pi}/3}, all correlation functions are (trivially) zero, for q=e{sup i{pi}/4}, they are related in the continuum to the correlation functions of left-handed and right-handed Majorana fields in the half plane coupled by the boundary condition. In the case q=e{sup i{pi}/6}, one gets the correlation functions of Mittag`s and Stephen`s parafermions for the three-state Potts model. A diagrammatic approach to compute correlation functions is also presented. (orig.)}
place = {Germany}
year = {1993}
month = {Oct}
}
title = {On the two-point correlation functions for the U{sub q}SU(2)invariant spin one-half Heisenberg chain at roots of unity}
author = {Hinrichsen, H, Martin, P P, Rittenberg, V, and Scheunert, M}
abstractNote = {Using U{sub q}SU(2) tensor calculus we compute the two-point scalar operators (TPSO), their averages on the ground-state give the two-point correlation functions. The TPSOs are identified as elements of the Temperley-Lieb algebra and a recurrence relation is given for them. We have not tempted to derive the analytic expressions for the correlation functions in the general case but got some partial results. For q=e{sup i{pi}/3}, all correlation functions are (trivially) zero, for q=e{sup i{pi}/4}, they are related in the continuum to the correlation functions of left-handed and right-handed Majorana fields in the half plane coupled by the boundary condition. In the case q=e{sup i{pi}/6}, one gets the correlation functions of Mittag`s and Stephen`s parafermions for the three-state Potts model. A diagrammatic approach to compute correlation functions is also presented. (orig.)}
place = {Germany}
year = {1993}
month = {Oct}
}