Abstract
The Raman spectrum of the two-dimensional Heisenberg model is discussed within Loudon-Fleury theory at both zero and finite temperature. The exact spectrum for lattices with up to sites is computed using Lanczös exact diagonalization. A quantum Monte Carlo (QMC) method is used to calculate the corresponding imaginary-time correlation function and its first two derivatives for lattices with up to spins. The imaginary-time data are continued to real frequency using the maximum-entropy method, as well as a fit based on spin-wave theory. The numerical results are compared with spin-wave calculations for finite lattices. There is a surprisingly large change in the exact spectrum going from to sites. In the former case there is a single dominant two-magnon peak at , whereas in the latter case there are two approximately equal-sized peaks at and . This is in good qualitative agreement with the spin-wave calculations including two-magnon processes on the same lattices. The spin-wave results for larger lattices show how additional peaks emerge with increasing lattice size, and eventually develop into the well known two-magnon profile peaked at and with weight extending up to . Both the Lanczös and the QMC results indicate that the actual two-magnon profile is broader than the narrow peak obtained in spin-wave theory, but the positions of the maxima agree to within a few percent. The higher-order contributions present in the numerical results are merged with the two-magnon profile and extend up to frequencies . The first three frequency cumulants of the spectrum are in excellent agreement with results previously obtained from a series expansion around the Ising limit. Typical experimental spectra for are only slightly broader than what we obtain here. The exchange constant extracted from the peak position is , in good agreement with values obtained from neutron scattering and NMR experiments. We discuss the implications of our present results for more sophisticated theories of Raman scattering suggested recently.
- Received 6 November 1997
DOI:https://doi.org/10.1103/PhysRevB.57.8478
©1998 American Physical Society