Quantum renormalization of high energy excitations in the 2 D Heisenberg antiferromagnet

We find using Monte Carlo simulations of the 2D square lattice nearest neighbour quantum Heisenberg anti-ferromagnet that the high energy peak locations at (π,0) and (π/2,π/2) differ by about 6%, (π/2,π/2) being the highest. This is a deviation from linear spin wave theory which predicts equal magnon energies at these points. It is also found that the peak at (π,0) is broader than the peak at (π/2,π/2). The simplest model describing quantum antiferromag-nets is the nearest neighbour quantum Heisenberg model. Among the class of materials which to a good accuracy can be described by this model are the undoped high-temperature superconductors where the strongly interacting quantum spins are located on a two-dimensional square lattice. Although simple to formulate the Heisen-berg model is not exactly solvable in dimensions greater than one, and approximations or numerical calculations is needed to compare the predictions of the Heisenberg model to experiments. While low-energy experiments such as measurements of the correlation length on undoped cuprates agree very well with the predictions of the Heisenberg model [1–3], the situation is more unclear at high energies. In particular, recent neutron scattering measurements on Cu(DCOO) 2 ·4D 2 O [4] and La 2 CuO 4 [5] directly probe the magnon dispersion between the two points (π/2,π/2) and (π,0) on the Brillouin zone boundary. These two materials, which are both considered to be physical realizations of the model system, show respectively a 6% decrease and a 13% increase in the magnon energy between (π/2,π/2) and (π,0). These results are in contrast to the linear spin-wave approximation of the 2D Heisenberg model, which predicts equal magnon-energies at these points. In this Letter we aim at clarifying the predictions of the S=1/2 Heisenberg model at high energies, in particular at the special points (π,0) and (π/2,π/2) in the Brillouin zone. The linear spin-wave approximation which is the ze-roth term in an expansion in the parameter 1/S gives the magnon spectrum ω k = 4JS 1 − γ 2 k , (1) where γ k = (cos k x + cos k y)/2. The wave-numbers are measured in units of the lattice spacing. Note that γ is zero both at (π,0) and (π/2,π/2). From Monte Carlo measurements it has been argued [6] that the only effect of the remaining terms in the expansion is to renormalize the coupling J by a factor Z(T), where Z(T = 0) = 1.183 for S = …