You need JavaScript to view this

On the two-point correlation functions for the U{sub q}SU(2)invariant spin one-half Heisenberg chain at roots of unity

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.)
Authors:
Hinrichsen, H; [1]  Martin, P P; [2]  Rittenberg, V; [1]  Scheunert, M [1] 
  1. Bonn Univ. (Germany). Physikalisches Inst.
  2. City Univ., London (United Kingdom). Dept. of Mathematics
Publication Date:
Oct 01, 1993
Product Type:
Technical Report
Report Number:
BONN-HE-93-35; HEP-TH-9310119
Reference Number:
SCA: 662120; PA: DEN-94:0F3790; EDB-94:058894; NTS-94:020504; SN: 94001179741
Resource Relation:
Other Information: PBD: Oct 1993
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; HEISENBERG MODEL; CORRELATION FUNCTIONS; SU-2 GROUPS; QUANTUM MECHANICS; FIELD ALGEBRA; BOUNDARY CONDITIONS; GROUND STATES; TENSORS; U GROUPS; EXPECTATION VALUE; RECURSION RELATIONS; SPINOR FIELDS; CHIRALITY; MAJORANA THEORY; PARASTATISTICS; FERMIONS; HAMILTONIANS; R MATRIX; TIME DEPENDENCE; FIELD OPERATORS; COMMUTATION RELATIONS; 662120; SYMMETRY, CONSERVATION LAWS, CURRENTS AND THEIR PROPERTIES
OSTI ID:
10140092
Research Organizations:
Bonn Univ. (Germany). Physikalisches Inst.
Country of Origin:
Germany
Language:
English
Other Identifying Numbers:
Journal ID: ISSN 0172-8733; Other: ON: DE94756188; TRN: DE94F3790
Availability:
OSTI; NTIS (US Sales Only); INIS
Submitting Site:
DEN
Size:
19 p.
Announcement Date:
Jul 05, 2005

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}
}