Signature of Néel order in exact spectra of quantum antiferromagnets on finite lattices

We show how the broken symmetries of the Néel state are embodied in the exact spectrum of the triangular Heisenberg antiferromagnet on finite lattices as small as N=21 (spectra up to N=36 have been computer). We present the first numerical evidence of an extensive set of low-lying levels that are below the softest magnons and collapse to the ground state in the thermodynamic limit. This set of quantum states represents the quantum counterpart of the classical Néel ground state. We develop an approach relying on the symmetry analysis and finite-size scaling and we provide new arguments in favor of an ordered ground state for the S=1/2 triangular Heisenberg model.