Describe physical system, history, models, single particle basis.
Specify Specific Model: Coulomb interaction at nu=1/3 on sphere
Use ED to compute energy spectra and wavefunctions. Plot Energy of few lowest eigenvalues as a function of total momentum. Identify roton.
Use ansatz wavefunction with variational Monte Carlo to compute lowest energies. Compare energies from ED with wavefunctions.
ED: generate basis generate, compute matrix elements, use eigenvalue solver, energy output, wavefunction output
VMC: construct wavefunction, construct interaction, do metropolis sampling, compute energy, bin energy, output with error bars