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Competing insulating phases in one-dimensional extended Hubbard models

Competing insulating phases in one-dimensional extended Hubbard models. Akira Furusaki (RIKEN) Collaborator: M. Tsuchiizu (Nagoya). M.T. & A.F., PRL 88, 056402 (2002) PRB 66, 245106 (2002) PRB 69, 035103 (2004). Contents.

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Competing insulating phases in one-dimensional extended Hubbard models

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  1. Competing insulating phases in one-dimensional extended Hubbard models Akira Furusaki (RIKEN) Collaborator: M. Tsuchiizu (Nagoya) M.T. & A.F., PRL 88, 056402 (2002) PRB 66, 245106 (2002) PRB 69, 035103 (2004) KIAS

  2. Contents One-dimensional models of interacting electrons at half filling • Extended Hubbard model • Ionic Hubbard model • Generalized Hubbard ladder Various types of insulators: Mott insulator, Charge-Density Wave, Peierls insulator, Band insulator, staggered-flux state, …. Weak-coupling approach, Bosonization KIAS

  3. t U V Extended Hubbard model at half filling KIAS

  4. Standard phase diagram (before 1999) Emery (1979) Hirsch (1984) Cannon, Scalettar, Fradkin (1991) ………. KIAS

  5. charge sector spin sector Spin sector Charge gap if Spin gap if Weak-coupling theory (g-ology) L R 1-loop RG KIAS

  6. Phase diagram since 1999 Discovery of Bond-charge-density wave (BCDW) phase or Bond-Order-Wave (BOW) Found numerically Nakamura (1999, 2000) Sengupta, Sandvik, Campbell (2002) ….. KIAS

  7. Vertex correction Degeneracy of zeros of and are lifted Separate transitions in charge & spin sectors In the strong-coupling regime 1st order SDW-CDW transition KIAS

  8. Tam, Tsai, & Campbell, cond-mat/0505396 KIAS

  9. Bosonization charge spin Order parameters KIAS

  10. Bosonized form of the Hamiltonian density kinetic energy marginal perturbation relevant perturbation irrelevant perturbation SU(2) symmetry etc KIAS

  11. Order parameters Classical analysis KIAS

  12. Phase transitions SDW-BCDW transition: 2nd order CDW-BCDW transition: 2nd order CDW-SDW transition:1st order KIAS

  13. Ground-state phase diagram from bosonization approach 1-loop RG + classical analysis M. Tsuchiizu and A.F., Phys. Rev. Lett. 88, 056402 (2002) KIAS

  14. Numerical Results Quantum Monte Carlo Sengupta, Sandvik, & Campbell, Phys. Rev. B 65, 155113 (2002) DMRG Y.G. Zhang, PRL 92, 246404 (2004) KIAS

  15. Sandvik, Balents & Campbell, PRL 92, 236401 (2004) • Tricritical point on the CDW-BCDW phase boundary SSE QMC Luttinger liquid parameter at the continuous transition KIAS

  16. umklapp scattering becomes relevant for KIAS

  17. Phase diagram (schematic) 1st order transition CDW-BCDW c=1 Gaussian SDW-BCDW c=1 SU(2)1 KIAS

  18. and Mott insulator and Band insulator Extended Ionic Hubbard model at half filling • Ionic Hubbard model Nagaosa & Takimoto (1986), Egami, Ishihara, & Tachiki (1993) Fabrizio, Gogolin, & Nersesyan, PRL 83, 2014 (1999) Quantum Phase Transition ? KIAS

  19. Ising KT 0 MI BI SDI Fabrizio, Gogolin, & Nersesyan, PRL 83, 2014 (1999) • Spontaneously Dimerized Insulating Phase (SDI) (= BCDW Phase) KIAS

  20. Extended ionic Hubbard model nearest-neighbor repulsion V Bosonization perturbative RG + classical analysis KIAS

  21. Bosonized form of the Hamiltonian density Kinetic energy marginal perturbation relevant perturbation irrelevant perturbation KIAS

  22. Classical analysis Gaussian Ising KIAS

  23. 1st order transition Ground-state phase diagram cf. KIAS

  24. Schematic phase diagrams KIAS

  25. V⊥, J⊥ tpair t⊥ Generalized Hubbard ladder at half filling KIAS

  26. Various Insulating Ground States that can appear in half-filled ladders rung singlet state (D-Mott) Ex. SO(5) ladder model charge density wave (CDW) ground-state phase diagram singlet paring state (S-Mott) staggered flux state (SF) Lin, Balents & Fisher (1998) Fjaerestad & Marston (2002) d-density wave orbital antiferromagnet KIAS

  27. Strong-coupling approach 4 basis states KIAS

  28. degenerate perturbation theory KIAS

  29. ordered state Ising model in a transverse field • CDW—S-Mott transition • D-Mott—S-Mott transition disordered state XXZ model in a magnetic field gapless (c=1) Gaussian transition KIAS

  30. Weak-coupling approach s-wave density wave order p-wave s-wave staggered dimerization p-wave d-wave d-wave f-wave d-density-wave =SF f-wave These states break Z2 symmetry KIAS

  31. Bosonization charge spin Hamiltonian density pinning potential Order parameters KIAS

  32. order disorder • Ising transitions Disorder parameters KIAS

  33. Ising transition (c=1/2) SU(2) criticality (c=3/2) 2 or 1st order transition Universality class of quantum phase transitions Gaussian transition (c=1) M. Tsuchiizu and A. Furusaki Phys. Rev. B 66, 245106 (2002) KIAS

  34. Duality transformation Momoi & Hikihara, PRL (2003) KIAS

  35. model V’ KIAS

  36. Summary • Competing interactions competing phases exotic order • Various (density) ordered phases • Various Mott insulating phases • 2D systems ? M.T. & A.F., PRL 88, 056402 (2002) PRB 66, 245106 (2002) PRB 69, 035103 (2004) KIAS

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