Valence-bond states: Link models

Enrique Rico (Corresponding author), Robert Hübener, Simone Montangero, Niall Moran, Bogdan Corneliu Pirvu, Jiri Vala, Hans-Jürgen Briegel

Publications: Contribution to journalArticlePeer Reviewed


An isotropic anti-ferromagnetic quantum state on a square lattice is characterized by symmetry arguments only. By construction, this quantum state is the result of an underlying valence bond structure without breaking any symmetry in the lattice or spin spaces. A detailed analysis of the correlations of the quantum state is given (using a mapping to a 2D classical statistical model and methods in field theory like mapping to the non-linear sigma model or bosonization techniques) as well as the results of numerical treatments (regarding exact diagonalization and variational methods). Finally, the physical relevance of the model is motivated. A comparison of the model to known anti-ferromagnetic Mott–Hubbard insulators is given by means of the two-point equal-time correlation function obtained (i) numerically from the suggested state and (ii) experimentally from neutron scattering on cuprates in the anti-ferromagnetic insulator phase.
Original languageEnglish
Pages (from-to)1875-1896
Number of pages22
JournalAnnals of Physics
Issue number9
Publication statusPublished - 2009

Austrian Fields of Science 2012

  • 103026 Quantum optics

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