Oct. 28, 2005 KIAS 12 J１～J2J１～J2 Exact diagonalization [Fouet et al., PRB 67, (2003)] J 1 =J 2, up to N=36 (N=40) ground state S=0: 2-fold degeneracy (N>>1) many low-lying excited states in the S=0 sector valence bond crystal (plaquette singlet)
Oct. 28, 2005 KIAS 13 Series expansion [Brenig and Grzeschik, PRB 69, (2004)] triplet dispersion
Oct. 28, 2005 KIAS 15 rewrite the Hamiltonian in terms of the T bosons discard quartic and higher-order terms quadratic approximation diagonalization by Bogoliubov transformation dispersion of triplet bosons (1) unstable when bosons condense at Antiferromagnetic LRO: Neel state (2) unstable when bosons condense at Magnetic LRO
Oct. 28, 2005 KIAS 23 Global phase diagram scenario I: direct transition between crossed-dimer and plaquette VBS NeelPlaquetteCrossed Dimer ?? ? = 1 st order transition or intermediate coexistence phase Continuous transitions are forbidden by Landau-Ginzburg-Wilson theory.
Oct. 28, 2005 KIAS 24 scenario II: crossed-dimer and plaquette VBS via an intermediate ordered phase ? ? Crossed DimerNeel*PlaquetteNeelO(3) ? = 1 st order transition or intermediate coexistence phase
Oct. 28, 2005 KIAS 25 application to 3d pyrochlore 3d crossed-dimer phase for
Oct. 28, 2005 KIAS 26 Summary Global phase diagram of the AF Heisenberg model on the 2d-pyrochlore (checkerboard lattice) 1d-approach can give some useful hints for understanding 2d and 3d frustrated magnets. NeelPlaquetteCrossed Dimer ?? PRB 72, (2005)
Oct. 28, 2005 KIAS 27 appendix uniform part of magnetization