Detecting spontaneous symmetry breaking in finite-size spectra of   frustrated quantum antiferromagnets
  Exact diagonalization is a powerful numerical technique to analyze static and dynamical quantities in quantum many-body lattice models. It provides unbiased information concerning quantum numbers, energies and wave-functions of the low-energy eigenstates for almost any kind of microscopic model. The information about energies and quantum numbers is particularly useful to detect possible spontaneous symmetry breaking at T=0. We review some of the advances in the field of frustrated quantum magnets which have been possible thanks to detailed symmetry analysis of exact diagonalizations spectra. New results concerning the kagome and star lattice Heisenberg antiferromagnets are presented. 
Gregoire Misguich, Philippe Sindzingre