Numerical investigation of correlation functions for the U_qSU(2) invariant spin-1/2 Heisenberg chain

Abstract

We consider the U q SU(2) invariant spin-1 2 XXZ quantum spin chain at roots of unity q = exp( i m+1 ), corresponding to di erent minimal models of conformal eld theory. We conduct a numerical investigation of correlation functions of U q SU(2) scalar twopoint operators in order to nd which operators in the minimal models they correspond to. Using graphical representations of the Temperley{Lieb algebra we are able to deal with chains of up to 28 sites. Depending on q the correlation functions show di erent characteristics and nite size behaviour. For m = 2 3 , which corresponds to the Lee{Yang edge singularity, we nd the surface and bulk critical exponent 1 5 . Together with the known result in the case m = 3 (Ising model) this indicates that in the continuum limit the two-point operators involve conformal elds of spin m 1 m+1 . For other roots of unity q the chains are too short to determine surface and bulk critical exponents.BONN TH 95-02 cond-mat/yymmnnn January 1995 1

A DMRG study of the -symmetric Heisenberg chain

“…The result of such a procedure for r = 5 is shown in figure 7. It proves that scaling is indeed fulfilled, in contrast to [20] where it could not be seen for chains up to L = 28. The exponent x for r = 3 then is only about 2% off the exact result x = 1/2.…”

“…The functions which we studied were q-symmetric generalizations of the quantity < σ l σ m > and correspond to fermionic and parafermionic correlators in the Ising and Potts case, respectively [19]. In a previous study with exact diagonalizations of short systems no conclusive results could be obtained for the Potts model [20]. From our calculations up to 100 sites we were able to obtain functions with clear scaling behaviour from which bulk and surface exponents could be extracted.…”

“…Due to the q-factor in (17) there is no symmetry between m and −m for q = 1 and the degeneracy of the eigenvalues is lifted as seen in figure 8. Specifically for large q one has c m ≃ q −(s−m) 2 (20) so that the coefficient c s ≃ 1 dominates and |Φ > becomes approximately a product state |Φ >≃ |s, s > 1 |s, −s > 2 .…”

Different facets of the raise and peel model

“…For the appearance of operators with conformal spin in the presence of the quantum group symmetry mentioned in section 3, see[38]. doi:10.1088/1742-5468/2007/07/P07009…”

Conformal invariance and its breaking in a stochastic model of a fluctuating interface

“…For the appearance of operators with conformal spin in the presence of the quantum group symmetry mentioned in the appendix, see[17]. doi:10.1088/1742-5468/2006/08/P08003…”