Mixed columnar-plaquette crystal of correlated fermions on the two-dimensional pyrochlore lattice at fractional filling

Physical Review B - Condensed Matter and Materials Physics

Volumn 78, Issue 19, 2008, Pages

  Trousselet, F ^a   Poilblanc, D ^a   Moessner, R ^b  

^a CNRS   (France)

^b MAX PLANCK INSTITUT FÜR PHYSIK KOMPLEXER SYSTEME   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 56349150060     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.78.195101     Document Type: Article

References (26)

1. B. Canals and C. Lacroix, Phys. Rev. Lett. 10.1103/PhysRevLett.80.2933 80, 2933 (1998).
2. J.-B. Fouet, M. Mambrini, P. Sindzingre, and C. Lhuillier, Phys. Rev. B 10.1103/PhysRevB.67.054411 67, 054411 (2003)
3. R. Moessner, O. Tchernyshyov, and S. L. Sondhi, J. Stat. Phys. 10.1023/B:JOSS.0000037247.54022.62 116, 755 (2004).
4. S. Wessel and M. Troyer, Phys. Rev. Lett. 10.1103/PhysRevLett.95.127205 95, 127205 (2005)
5. D. Heidarian and K. Damle, Phys. Rev. Lett. 10.1103/PhysRevLett.95.127206 95, 127206 (2005)
6. R. G. Melko, A. Paramekanti, A. A. Burkov, A. Vishwanath, D. N. Sheng, and L. Balents, Phys. Rev. Lett. 10.1103/PhysRevLett.95.127207 95, 127207 (2005)
7. A. Sen, P. Dutt, K. Damle, and R. Moessner, Phys. Rev. Lett. 10.1103/PhysRevLett.100.147204 100, 147204 (2008).
8. A. Sen, K. Damle, and T. Senthil, Phys. Rev. B 10.1103/PhysRevB.76.235107 76, 235107 (2007).
9. F. Pollmann, J. J. Betouras, K. Shtengel, and P. Fulde, Phys. Rev. Lett. 10.1103/PhysRevLett.97.170407 97, 170407 (2006)
10. F. Pollmann, P. Fulde, and E. Runge, Phys. Rev. B 10.1103/PhysRevB.73. 125121 73, 125121 (2006).
11. P. Fulde, K. Penc, and N. Shannon, Ann. Phys. 11, 892 (2002). 10.1002/1521-3889(200212)11:12<892::AID-ANDP892>3.0.CO;2-J
12. D. S. Rokhsar and S. A. Kivelson, Phys. Rev. Lett. 10.1103/PhysRevLett. 61.2376 61, 2376 (1988).
13. R. Moessner and S. L. Sondhi, Phys. Rev. B 10.1103/PhysRevB.68.054405 68, 054405 (2003).
14. D. Poilblanc, K. Penc, and N. Shannon, Phys. Rev. B 10.1103/PhysRevB.75. 220503 75, 220503 (R) (2007).
15. D. Poilblanc, Phys. Rev. B 10.1103/PhysRevB.76.115104 76, 115104 (R) (2007).
16. S. Wessel, Phys. Rev. B 10.1103/PhysRevB.78.075112 78, 075112 (2008).
17. M. Indergand, C. Honerkamp, A. Läuchli, D. Poilblanc, and M. Sigrist, Phys. Rev. B 10.1103/PhysRevB.75.045105 75, 045105 (2007).
18. A. Ralko, D. Poilblanc, and R. Moessner, Phys. Rev. Lett. 10.1103/PhysRevLett.100.037201 100, 037201 (2008).
19. For an N=72 cluster with PBC, the Hilbert space, as defined previously (using spin inversion, point-group symmetries, and translations keeping invariant each sublattice of the dimer lattice) in the most symmetric sector (A1,q=0) has 192790 configurations; for t2 =1 and W=-2, the energy of the ground state is EGS =-62.63747973...
20. O. A. Starykh, A. Furusaki, and L. Balents, Phys. Rev. B 10.1103/PhysRevB.72.094416 72, 094416 (2005).
21. F. H. L. Essler, A. M. Tsvelik, and G. Delfino, Phys. Rev. B 10.1103/PhysRevB.56.11001 56, 11001 (1997).
22. For the W=0 case (derived from the extended Hubbard model), the energy per particle of the RSPC (and MCPC-2) variational wave function in units of t2 is E=-1, while the exact values on periodic clusters are respectively N=32, 48, 64 and 72 are respectively (given with 0.001 precision): -1.166;-1.136;-1.088;- 1.099. (The two last clusters being oriented at π/4 from each other, the relative position of their ground-state energies is not anormal). A rough estimate would give E=-1.06 (2) in the thermodynamic limit.
23. Close to W= t2 and in the thermodynamic limit, the RK wave function has an energy of 2 (W- t2) nfl per uncrossed plaquette (so twice as much per particle), where nfl, the probability for a given plaquette to be flippable, equals 1/4. Similarly, in the bosonic case, the flippability is nfl =1/4 and the energy of the RK state equals (V-t) /2 per particle.
24. Using the spin inversion symmetry allows one to compute eigenstates and eigenenergies in sectors of total spin either odd or even, but not explicitly in the S=0 or S=1 sector. However it is known that states of lowest energy are of total spin S=0 or S=1.
25. Two clusters of size N=80 would be tractable by exact diagonalization, but there either the π/2 rotation symmetry or the reflexion symmetry would be lost (in comparison to the N=64 cluster for instance) which would be problematic for determining the quantum numbers characterizing the phases of the model. The next cluster available (by increasing N) and possessing these symmetries would be the N=128 cluster, far beyond the limits of existing numerical resources for exact diagonalizations.
26. D. Poilblanc, Phys. Rev. Lett. 10.1103/PhysRevLett.93.197204 93, 197204 (2004).