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Cristian D. Batista and Stuart A. Trugman T-11 Los Alamos National Laboratory

Exact ground states of a frustrated 2D magnet: deconfined fractional excitations at a first order quantum phase transition. Cristian D. Batista and Stuart A. Trugman T-11 Los Alamos National Laboratory Los Alamos, NM - USA. Cond-mat/047216. Outline. -General Motivation.

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Cristian D. Batista and Stuart A. Trugman T-11 Los Alamos National Laboratory

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  1. Exact ground states of a frustrated 2D magnet: deconfined fractional excitations at a first order quantum phase transition Cristian D. Batista and Stuart A. Trugman T-11 Los Alamos National Laboratory Los Alamos, NM - USA Cond-mat/047216

  2. Outline -General Motivation. -Model for a frustrated 2D Magnet. -Exact Ground States: Valence bond crystal with soft 1D topological defects. -Excitations:Spinons propagating along 1D paths. Spin charge separation for one hole added. -Identification of the solvable point with a first order QPT. -Extensions to other 2D lattices. -Conclusions.

  3. Introduction H= J1 Si .Sj + J2  Si .Sj i , j i , j AFM AFM (, ) (,) Valence Bond Crystal ( N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991).) O.P. ? J2 /J1 1/2 Uniform Spin Liquid (P. Fazekas and P. W. Anderson, Philos. Mag. 80, 1483 (1974).)

  4. Introduction Proposals for deconfined points in frustrated magnets O.P. O.P. H= Jij Si.Sj + … Roksar-Kivelson model VBC I AF VBC VBC II g QCP QCP T. Senthil et al, Science 303, 1490 (2003) Moessner et al, Phys.Rev. B65 024504(2002) E. Fradkin et al, Phys. Rev.B69, 224415 (2004) A. Vishwanath et al, Phys. Rev.B69, 224416 (2004)

  5. Introduction AFM AFM (, ) (,) Proposals for deconfined points in frustrated magnets Confederate Flag model VBC I VBC II 0 x QCP A.M. Tsvelik, cond-mat/0404541 (2004) A.A. Neresyan and A. M. Tsvelik, Phys. Rev. B 67, 024422 (2003)

  6. Hamiltonian H= J1 Si .Sj + J2  Si .Sj + K  (Pij Pkl+ Pjk Pil+ Pik Pjl) i , j i , j        i j This sign is negative in the usual four-cyclic exchange term.  k l

  7. Hamiltonian Hp=(3J1 /2) P   Hp=H(J2=J1 /2, K=J1 /8) P  is the projector on the S =2 subspace. S   1 = singlet dimer

  8. Ground States

  9. Ground States: Defects

  10. Ground States: Defects

  11. Low Energy Excitations x x x x x x x x Deconfined Confined

  12. Low Energy Excitations x x x x x x x x Doped System: Spin-Charge separation

  13. First Order Quantum Phase Transition 4-fold degeneracy 8-fold degeneracy OP ZD SD 0 g

  14. General Transition Ol+1 Ol Ol+2 Ol+4 Ol +3 Ol+5 ….. . . . . . . . . . . - - - - - - - q=0

  15. General Transition Ol+1 Ol Ol+2 Ol+4 Ol +3 Ol+5 ….. . . . . . . . . . . + + + + + + + q=

  16. Extensions to other Lattices Hp= Q ,  where Q is the projector on the S=2,3 subspace.

  17. Conclusions: A Valence Bond Crystal is exactly obtained for the fully frustrated Heisenberg model on a square lattice in the presence of a small four-spin term (K=J1/8). The ground states and the excitations exhibit exotic behaviors like the softening of 1D topological defects and the emergence of deconfined spinons. This point can be identified with a first order QPT.

  18. Conclusions: There is spin-charge separation when the system is doped with one hole. The common origin of the exotic behaviors is a dynamical decoupling of the 2D magnet into 1D systems. Questions: Finite concentration of holes and anisotropic conductivity? Effect of finite temperature? - What is the effect of reducing K?

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