Hardcore Magnons in the S=1/2 Heisenberg Model on the Square Lattice

Abstract

We propose a versatile approach to treat commonly arising constraints. It is illustrated for interacting magnons of the Heisenberg antiferromagnet on a square lattice. For systems of $L\times L$ sites a non-perturbative continuous unitary transformation (CUT) is used to derive an effective Hamiltonian conserving the number of magnons. They are bosonic particles with a hardcore constraint which is captured by a local, repulsive interaction U. The limits $U\to \infty$ and $L\to \infty$ are achieved by extrapolation. The residual spin gap ${\Delta }_1$ is smaller than 0.01J reflecting the gapless nature of the magnons. The one-magnon dispersion displays all known characteristics.

arXiv comment4 pages, 3 figures

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Cited by in corpus (3)

• Two-particle bound states and one-particle structure factor in a Heisenberg bilayer system
• Continuous similarity transformation for critical phenomena: easy-axis antiferromagnetic XXZ model
• Quantum melting of long-range ordered quantum antiferromagnets investigated by momentum-space continuous similarity transformations