Title

Quantum Spin Chains and the Conformal Anomaly

Authors

Jill C. Bonner, University of Rhode Island
John B. Parkinson

Document Type

Article

Date of Original Version

1988

Abstract

The conformal anomaly c determines the universality class of a model system in statistical mechanics. The value of c characterizes both 2D classical models and their 1D quantum counterparts. The conformal anomaly may therefore be determined numerically for quantum spin chains using the relation: E ₀(N)≂E ₀(∞)−(NΔE/12)c(1/N ²), where E ₀ (N) is the ground‐state energy of an N‐spin finite system, E ₀ (∞) is the ground‐state energy in the thermodynamic limit, and ΔE is the energy gap between the ground state at k=0 and the first excited state of the dispersion curve at k=2π/N. The numerical approach is highly successful when tested on the integrable s= 1/2 Heisenberg antiferromagnetic X X Z chain and the integrable s=1 SU(2) model. The method gives c=1 to within 2% accuracy for the s=1 and (3)/(2) X Y chains, placing them in the universality class of the 2D X Y model. The result c=1 (2% accuracy) is obtained for the s= (3)/(2) Heisenberg antiferromagnetic chain, in agreement with the Haldane prediction. The s=1 pure antiferromagnetic biquadratic chain and the s=1 X X Z model with uniaxial anisotropy in the vicinity of the critical point Δ=Δ₂ ∼1.15 −1.18 have also been studied.

Citation/Publisher Attribution

Jill C. Bonner and John B. Parkinson. Quantum spin chains and the conformal anomaly. J. Appl. Phys. 63 (1988), 3543-3545.

Available at http://dx.doi.org/10.1063/1.340737.

Publisher Statement

Copyright 1988 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.

The following article appeared in Journal of Applied Physics and may be found at http://dx.doi.org/10.1063/1.340737.