Symmetry breaking in quantum antiferromagnets on a triangular lattice

W.J. Caspers, G.I. Tielen

Sedigh Ghamari, Catherine Kallin, Sung-Sik Lee

B. Bernu, P. Lecheminant, C. Lhuillier +1 more

We have realized a thorough quantum mechanical analysis of an extensive number of low lying levels of the Heisenberg Hamiltonian on small periodic samples. Striking qualitative differences appear between the spectra of the triangular lattice and those of the Kagomé lattice. Symmetries and finite size scaling of the low lying levels of the triangular antiferromagnetic point to an à la Néel symmetry breaking, and the dynamical structure factors corroborate this conclusion. The Kagomé antiferromagnet spectra are qualitatively different: no signature of a symmetry breaking has been exhibited and the dynamical structure factors of the low lying levels display broad bands. The Heisenberg antiferromagnet on a Kagomé lattice is a serious candidate for a spin liquid.

Tohru Koma, Hal Tasaki

Tomo Munehisa, Yasuko Munehisa

Motivated by recent experiments that require more complicated macroscopic wave functions in the condensed matters, we make numerical study on a XY quantum antiferromagnet on a finite triangular lattice using the variational Monte Carlo method and the stochastic state selection method. One of our purpose is a numerical confirmation on dominance of a Nambu-Goldstone boson in low energy excitation. For another purpose, we calculate energy, an expectation value of a symmetry breaking operator and structure functions of spin by fixing a quantum number of the symmetry. These calculations are made for states that become degenerate in an infinitely large lattice. By numerical calculations we confirm existence of a Nambu-Goldstone boson, and find dependence of a square of the quantum number for the above quantities. Using these results we can discuss on complicated macroscopic wave functions in quantum spin systems.

P. Azaria, Bertrand Delamotte, D. Mouhanna

We show that the spontaneous symmetry breaking mechanism in quantum antiferromagnets is due to the collapse, in the thermodynamical limit, of an infinite set of excited states onto the ground state. We characterize both the nature and the scaling of the relevant tower of states for the quantum antiferromagnet on the triangular lattice. Comparison with recent numerical results for the S=1/2 case gives strong support for the existence of long range order in this system.