Phys. Rev. B 48, 1028 (1993)

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Real-space renormalization-group studies of low-dimensional quantum antiferromagnets

Marie-Bernadette Lepetit

Laboratoire de Physique Quantique, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse CEDEX, France

Efstratios Manousakis

Department of Physics, Center for Materials Research and Technology Supercomputer Computations Research Isntitute, Florida State University, Tallahassee, Florida 32306

We study the ground state of one- and two-dimensional (square-lattice) spin-1/2 quantum antiferromagnets using a numerical real-space renormalization-group (RG) approach. In our RG approach we consider blocks of various sizes but with an odd number of sites; we retain only the doublet ground state and we integrate out the higher-energy states by means of second-order quasidegenerate perturbation theory. That is, we assume that the role of the excited states of a block, in the RG iteration process, is to renormalize the effective coupling parameters between blocks. We compute the ground-state energy of a spin-1/2 linear chain for various block sizes and find close agreement with the Bethe-ansatz exact solution. In the case of the spin-1/2 square-lattice quantum antiferromagnet, the obtained ground-state energy is in reasonable agreement with the available numerical estimates.

©1993 The American Physical Society.

PACS: 71.10.+x 75.10.Jm

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