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

4. Introduction Proposals for deconfined points in frustrated magnets AF VBC QCP O.P. g T. Senthil et al, Science 303, 1490 (2003) O.P. H= J   ij  S i.S j + … VBC I VBC II QCP Roksar-Kivelson model 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 Proposals for deconfined points in frustrated magnets VBC I QCP A.M. Tsvelik, cond-mat/0404541 (2004) A.A. Neresyan and A. M. Tsvelik, Phys. Rev. B 67, 024422 (2003) VBC II AFM (,)(,) x 0 ( ,  ) AFM Confederate Flag model

6. H = J 1  S i.S j + J 2  S i.S j + K  (P ij P kl + P jk P il + P ik P jl )     i, j   i, j   ij kl  Hamiltonian This sign is negative in the usual four-cyclic exchange term.

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

8. Ground States

9. Ground States: Defects

11. Low Energy Excitations x x x x x x x x DeconfinedConfined

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

13. First Order Quantum Phase Transition OP g0 SD ZD 4-fold degeneracy 8-fold degeneracy

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

15. General Transition OlOl O l+1 O l+2 O l +3 O l+4 O l+5 …....... + + ++ ++ + q=q=

16. Extensions to other Lattices  H p =  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=J 1 /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?