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Entropy-driven first-order phase transition in quantum compass model with Ly>3

Entropy-driven first-order phase transition in quantum compass model with Ly>3. Tian Liang. Orbital compass model with directional coupling. K. I. Kugel and D. I. Khomskii, Sov. Phys. JETP 37 , 725 (1973). Y. Tokuraand N. Nagaosa, Science 288 , 462 (2000)

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Entropy-driven first-order phase transition in quantum compass model with Ly>3

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  1. Entropy-driven first-order phase transition in quantum compass model with Ly>3 Tian Liang

  2. Orbital compass model with directional coupling K. I. Kugel and D. I. Khomskii, Sov. Phys. JETP 37, 725 (1973). Y. Tokuraand N. Nagaosa, Science 288, 462 (2000) D. I. Khomskiiand M. V. Mostovoy, J. Phys. A 36, 9197 (2003) J. van den Brink, New J. Phys. 6, 201 (2004) J.B. Kogut, RMP 51, 659 (1979) Z. Nussinovand E. Fradkin, PRB 71, 195120 (2005) J. E. Moore and D.-H. Lee, PRB 69, 104511 (2004) A. Yu Kitaev, Ann. Phys. (N.Y.) 303, 2 (2003) L.B. Ioffeet al., Nature 415, 503 (2002) B. Douçotet al., PRB 71, 024505 (2005) A. Micheli, G.K. Brennenand P. Zoller, Nature Physics 2, 341 (2006) C.K. Xuand M. P. A. Fisher, PRB 75, 104428 (2007) `

  3. DUALITY TRANSFORMATION Compass model Plaquette model

  4. The plaquette model quantum fluctuation h = 0: classical model of Ising spins one-dimensional nearest-neighbor Ising model Symmetry: system energy remains the same under spin flip for each row and each column Ground state degeneracy: Given arbitrary values of the spins on one row and one column, there is a unique ground of the system compatible with these values. h > Kxy: quantum fluctuations leads to proliferation of defects and loss of long-ranged order.

  5. QUANTUM-CLASSICAL MAPPING Path integral representation Self-duality

  6. Numerical ResultsTwo chain problem: Ly=2

  7. Finite size scaling 2D Ising model γ= 1.75 β =0.125 ν = 1

  8. Numerical ResultsTwo chain problem: Ly=3

  9. Finite size scaling Four-state Potts model α = 0.69 γ = 1.17 β =0.085 ν = 0.66

  10. the nature of the disorder transition B. Doucot et al., PRB 71, 024505 (2005) S. Wenzel and W. Janke, cond-mat/0804.2972v1

  11. Numerical ResultsTwo chain problem: Ly=4

  12. Numerical ResultsTwo chain problem: Ly=Lx (Quantum 2D system )

  13. First-order phase transitionfor Ly>3

  14. q-state Potts model and coloring entropy continuous Line tension, vanishes at t = 0 Coloring entropy (q>4) mosaic

  15. q-state Potts & XY model and coloring entropyvs.Four color theorem The current work

  16. The end

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