Detecting spontaneous symmetry breaking in finite-size spectra of frustrated quantum antiferromagnets

Abstract

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.

Proceedings of the International Conference "Highly Frustrated Magnets", Osaka (Japan), August 2006). Version 2 (Published): Added figure with the valence-bond crystal on the expanded kagome lattice, and minor changes in the text. Version 3: Corrected an ambiguity in column 'VBC-1' of Table 1 (+caption)

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• Nematic order in square lattice frustrated ferromagnets
• Twelve sublattice ordered phase in the J1-J2 model on the kagome lattice
• Absence of magnetic order for the spin-half Heisenberg antiferromagnet on the star lattice
• Quantum Phase Transition in the SU(4) Spin-Orbital Model on the Triangular Lattice
• Spin-Charge Separation in Two-dimensional Frustrated Quantum Magnets
• Systematic Derivation of Order Parameters through Reduced Density Matrices

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• Competing Valence Bond Crystals in the Kagome Quantum Dimer Model
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