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arXiv:0811.0526 · The European Physical Journal B

Real space renormalization group approach to the two-dimensional antiferromagnetic Heisenberg model (I) – The singlet triplet gap

Andreas Fledderjohann, Andreas Klümper, K.-H. Mütter

Published Nov 7, 2009• 1 citation
arXivHTMLPDF
DOI
10.1140/epjb/e2009-00381-2

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The ground-state energy and the singlet-triplet energy gap of the antiferromagnetic Heisenberg model on a ladder is investigated using a mean-field theory and the density-matrix renormalization group. Spin-wave theory shows that the corrections to the local magnetization are infinite. This indicates that no long-range order occurs in this system. A flux-phase state is used to calculate the energy gap as a function of the transverse coupling, ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$, in the ladder. It is found that the gap is linear in ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$ for ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$\ensuremath{\gg}1 and goes to zero for ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$\ensuremath{\rightarrow}0. The mean-field theory agrees well with the numerical results.
We numerically study the spin-1/2 antiferromagnetic Heisenberg model on the kagome lattice using the density-matrix renormalization group method. We find that the ground state is a magnetically disordered spin liquid, characterized by an exponential decay of spin-spin correlation function in real space and a magnetic structure factor showing system-size independent peaks at commensurate magnetic wave vectors. We obtain a spin triplet excitation gap DeltaE(S=1)=0.055+/-0.005 by extrapolation based on the large size results, and confirm the presence of gapless singlet excitations. The physical nature of such an exotic spin liquid is also discussed.
We numerically study the spin-1/2 antiferromagnetic Heisenberg model on the kagomé lattice using the density-matrix renormalization group (DMRG) method. We find that the ground state is a magnetically disordered spin liquid, characterized by an exponential decay of spin-spin correlation function in real space and a magnetic structure factor showing system-size independent peaks at commersurate antiferromangetic wavevectors. We obtain a spin triplet excitation gap ΔE(S=1)=0.055±0.005ΔE(S=1)=0.055\pm 0.005ΔE(S=1)=0.055±0.005 by extrapolation based on the large size results, and confirm the presence of gapless singlet excitations. The physical nature of such an exotic spin liquid is also discussed.