The Matrix Product Approach to Quantum Spin Ladders

Abstract

We present a manifestly rotational invariant formulation of the matrix product method valid for spin chains and ladders. We apply it to 2 legged spin ladders with spins 1/2, 1 and 3/2 and different magnetic structures labelled by the exchange coupling constants, which can be ferromagnetic or antiferromagnetic along the legs and the rungs of the ladder We compute ground state energy densities, correlation lengths and string order parameters. We present numerical evidence of the duality properties of the 3 different non ferromagnetic spin 1/2 ladders. We show that the long range topological order characteristic of isolated spin 1 chains is broken by the interchain coupling. The string order correlation function decays exponentially with a finite correlation length that we compute. A physical picture of the spin 1 ladder is given in terms of a collection of resonating spin 1 chains. Finally for ladders with spin equal or greater than 3/2 we define a class of AKLT states whose matrix product coefficients are given by 9-j symbols.

REVTEX file, 16 pages, 12 figures, 6 Tables

References in corpus (3)

• Equivalence of the Variational Matrix Product Method and the Density Matrix Renormalization Group applied to Spin Chains
• The Short Range RVB State of Even Spin Ladders: A Recurrent Variational Approach
• Dualities in Spin Ladders

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