  The B1g Raman spectrum of the two-dimensional S=1/2 Heisenberg model is
discussed within Loudon-Fleury theory at both zero and finite temperature. The
exact T=0 spectrum for lattices with up to 6*6 sites is computed using Lanczos
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 16*16 spins. The imaginary-time data is
continued to real frequency using the maximum-entropy method, as well as a fit
based on spinwave theory. The numerical results are compared with spinwave
calculations for finite lattices. There is a surprisingly large change in the
exact spectrum going from 4*4 to 6*6 sites. In the former case there is a
single dominant two-magnon peak at frequency w/J appr. 3.0, whereas in the
latter case there are two approximately equal-sized peaks at w/J appr. 2.7 and
3.9. This is in good qualitative agreement with the spinwave calculations
including two-magnon processes on the same lattices. Both the Lanczos and the
QMC results indicate that the actual infinite-size two-magnon profile is
broader than the narrow peak obtained in spinwave 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 w/J appr. 7. 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 B1g$ spectra for
La2CuO4 are only slightly broader than what we obtain here. The exchange
constant extracted from the peak position is J appr. 1400K, in good agreement
with values obtained from neutron scattering and NMR experiments.
