Title: Exact diagonalization study on spin-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:mfrac></mml:math>ladders as a function of two coupling parameters using the symmetric group approach
Abstract: Using the symmetric-group-approach method [N. Flocke and J. Karwowski, Phys. Rev. B 55, 8287 (1997)], exact diagonalization studies on a set of spin-1/2 Heisenberg ladders containing three different couplings $J$, ${J}^{\ensuremath{'}}$ (chain), and ${J}_{\ensuremath{\perp}}$ (rungs) were performed and the behavior of the singlet-triplet energy gap was analyzed as a function of ${J}^{\ensuremath{'}}$ and ${J}_{\ensuremath{\perp}}$ in units of $J$. Exact diagonalizations for the ground and first-exited state were performed for up to $2\ifmmode\times\else\texttimes\fi{}L=30$ spins for the isotropic ladder ${(J=J}^{\ensuremath{'}}{=J}_{\ensuremath{\perp}})$ and for up to $2\ifmmode\times\else\texttimes\fi{}L=28$ spins for all the anisotropic ones. All calculations were done under periodic/M\"obius boundary conditions for $L$ even/odd, respectively. I found some evidence, that for certain ${J}_{\ensuremath{\perp}},$ ${J}^{\ensuremath{'}}$ pairs the gap may vanish in the bulk limit. For the isotropic ladder I obtained for the gap $\ensuremath{\Delta}(\ensuremath{\infty})=0.49996$, giving further support for the conjecture that for this system the exact value of $\ensuremath{\Delta}(\ensuremath{\infty})$ is equal to 1/2.
Publication Year: 1997
Publication Date: 1997-12-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 10
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