We consider the U q SU(2) invariant spin-1/2 XXZ quantum spin chain at the roots of unity q=exp(i pi /(m+1)), corresponding to different minimal models of conformal field theory. We conduct a numerical investigation of the correlation functions of U q SU(2) scalar two-point operators in order to find 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 different characteristics and finite-size behaviour. For m=2/3, which corresponds to the Lee-Yang edge singularity, we find 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 fields of spin-m-1/m+1. For other roots of unity q the chains are too short to determine the surface and bulk critical exponents.We consider the U q SU(2) invariant spin-1/2 XXZ quantum spin chain at the roots of unity q=exp(i pi /(m+1)), corresponding to different minimal models of conformal field theory. We conduct a numerical investigation of the correlation functions of U q SU(2) scalar two-point operators in order to find 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 different characteristics and finite-size behaviour. For m=2/3, which corresponds to the Lee-Yang edge singularity, we find 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 fields of spin-m-1/m+1. For other roots of unity q the chains are too short to determine the surface and bulk critical exponents.

arXiv:cond-mat/9501035Journal of Physics A Mathematical and GeneralJul 7, 19953 citations

Dynamical correlation functions of a two-spin operator in quantum spin chains

Matheus Schossler, Rodrigo G. Pereira

Livro de ResumosJan 1, 20160 citations

Affine Quantum Groups and Quantum Spin Chains

Akishi Kato

Mar 20, 19940 citations

Loop symmetry of integrable vertex models at roots of unity

Korff, C, Barry M. McCoy

It has been recently discovered in the context of the six vertex or XXZ model in the fundamental representation that new symmetries arise when the anisotropy parameter $(q+q^{-1})/2$ is evaluated at roots of unity $q^{N}=1$ . These new symmetries have been linked to an $U(A^{(1)}_1)$ invariance of the transfer matrix and the corresponding spin-chain Hamiltonian.In this paper these results are generalized for odd primitive roots of unity to all vertex models associated with trigonometric solutions of the Yang-Baxter equation by invoking representation independent methods which only take the algebraic structure of the underlying quantum groups $U_q(\\hat g)$ into account. Here $\\hat g$ is an arbitrary Kac-Moody algebra. Employing the notion of the boost operator it is then found that the Hamiltonian and the transfer matrix of the integrable model are invariant under the action of $U(\\hat{g})$ . For the simplest case $\\hat g=A_1^{(1)}$ the discussion is also extended to even primitive roots of unity.It has been recently discovered in the context of the six vertex or XXZ model in the fundamental representation that new symmetries arise when the anisotropy parameter $(q+q^{-1})/2$ is evaluated at roots of unity $q^{N}=1$. These new symmetries have been linked to an $U(A^{(1)}_1)$ invariance of the transfer matrix and the corresponding spin-chain Hamiltonian.In this paper these results are generalized for odd primitive roots of unity to all vertex models associated with trigonometric solutions of the Yang-Baxter equation by invoking representation independent methods which only take the algebraic structure of the underlying quantum groups $U_q(\\hat g)$ into account. Here $\\hat g$ is an arbitrary Kac-Moody algebra. Employing the notion of the boost operator it is then found that the Hamiltonian and the transfer matrix of the integrable model are invariant under the action of $U(\\hat{g})$. For the simplest case $\\hat g=A_1^{(1)}$ the discussion is also extended to even primitive roots of unity.

Jan 1, 200113 citations

It has been recently discovered in the context of the six vertex or XXZ model in the fundamental representation that new symmetries arise when the anisotropy parameter

(q+q^{-1})/2

is evaluated at roots of unity

q^{N}=1

. These new symmetries have been linked to an

U(A^{(1)}_1)

invariance of the transfer matrix and the corresponding spin-chain Hamiltonian.In this paper these results are generalized for odd primitive roots of unity to all vertex models associated with trigonometric solutions of the Yang-Baxter equation by invoking representation independent methods which only take the algebraic structure of the underlying quantum groups

U_q(\\hat g)

into account. Here

\\hat g

is an arbitrary Kac-Moody algebra. Employing the notion of the boost operator it is then found that the Hamiltonian and the transfer matrix of the integrable model are invariant under the action of

U(\\hat{g})

. For the simplest case

\\hat g=A_1^{(1)}

the discussion is also extended to even primitive roots of unity.