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Chiral Spin States in the Pyrochlore Heisenberg Magnet

Chiral Spin States in the Pyrochlore Heisenberg Magnet. Jung Hoon Kim & Jung Hoon Han Department of Physics, Sungkyunkwan University, Korea arXiv : 0807.2036. Antiferromagnet. Ferromagnet. Introduction. We would like to better understand the quantum ground state

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Chiral Spin States in the Pyrochlore Heisenberg Magnet

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  1. Chiral Spin States in the Pyrochlore Heisenberg Magnet Jung Hoon Kim & Jung Hoon Han Department of Physics, Sungkyunkwan University, Korea arXiv : 0807.2036

  2. Antiferromagnet Ferromagnet Introduction • We would like to better understand the quantum ground state of the spin-1/2 Heisenberg Hamiltonian on the pyrochlore lattice • Frustrated Systems : - Systems in which all interactions cannot be simultaneously satisfied Can lead to exotic phases and completely different ground states

  3. Introduction (2) • Highly Frustrated Systems Kagome Lattice Pyrochlore Lattice

  4. Mean-field Analysis • Solve the Heisenberg Hamiltonian within fermionic mean-field theory • Rewrite spin operators as fermion bilinears Terms of 4 interacting fermions

  5. - Allowed states constraint : Mean-field Analysis • Apply mean-field theory (consider hopping terms only : ) • Interested in spin-1/2 systems

  6. . . . 0 Mean-field Analysis • For the half-filled case : • Project out doubly occupied states by Gutzwiller projection Tractable by numerical analysis (Variational Monte Carlo)

  7. 3 2 1 Flux States - Kagome • Possible flux states (Kagome) : • Rokhsar’s theorem Rokhsar PRL 65, 1506 (1990)

  8. 3 2 1 Flux States - Kagome • Possible flux states (Kagome) : Ran et al. PRL 98, 117205 Hermele et al. arxiv:0803.1150v2

  9. Flux States - Pyrochlore Jung Hoon Kim and Jung Hoon Han arXiv 0807.2036 2 1 3 4 1 3 2

  10. Flux States - Pyrochlore 12 11 16 9 10 4 15 13 14 3 1 8 2 5 7 6

  11. 2 1 3 4 1 3 Flux States - Pyrochlore 2

  12. 12 16 11 9 10 4 15 13 14 3 1 8 2 5 7 6 Flux States - Pyrochlore

  13. Summary • Fermionic mean-field theory and variational Monte Carlo techniques have been employed to understand the nature of the ground state of the spin-1/2 Heisenberg model on the pyrochlore lattice. • From VMC calculations, of the four different flux states considered, the [/2,/2,0]-flux state had the lowest energy. • Although the [/2,/2,0]-flux state had the lowest energy, the [/2,-/2,0]-flux state is the more stable state, as can be seen from the band structure. • Due to the rapid decrease of the spin-spin correlation and small lattice sizes considered, it was hard to distinguish between a power law and exponential decay of the spin-spin correlation function. • The two flux states, [/2,/2,0] and [/2,-/2,0], have non-zero expectation values of the scalar chirality, , showing that they are indeed chiral flux states (i.e. states with broken time-reversal symmetry).

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