Quantum magnetism on the Cairo pentagonal lattice

Physical Review B - Condensed Matter and Materials Physics

Volumn 85, Issue 10, 2012, Pages

  Rousochatzakis, I ^a,b   Lauchli A M ^a,c   Moessner, R ^a  

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

^b Institute for Theoretical Solid State Physics   (Germany)

^c UNIVERSITY OF INNSBRUCK   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84859051452     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.85.104415     Document Type: Article

References (61)

1. Introduction to Frustrated Magnetism, edited by C. Lacroix, P. Mendels, and F. Mila, Springer Series in Solid-State Sciences, Vol. 164 (Springer, Berlin, 2011).
2. Frustrated Spin Systems, edited by H. T. Diep (World Scientific, Singapore, 2004).
3. J. Richter, J. Schulenburg, and A. Honecker, in Quantum Magnetism, edited by, U. Schollwöck, J. Richter, D. J. J. Farnell, and, R.F. Bishop, Lect. Notes Phys. 645 (Springer, Berlin, 2004), Chap. 2.
4. H-J. Schmidt and M. Luban, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/36/23/306 36, 6351 (2003).
5. J. Kepler, Harmonices Mundi (J. Planck for G. Tampach, Linz, Austria, 1619).
6. B. Grünbaum and G. C. Shephard, Tilings and Patterns (Freeman, New York, 1987).
7. M. Gardner, Tiling with Convex Polygons, in Time Travel and Other Mathematical Bewilderments (Freeman, New York, 1988).
8. R. Moessner and S. L. Sondhi, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.63.224401 63, 224401 (2001).
9. V. Urumov, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/35/34/306 35, 7317 (2002). (Pubitemid 37049291)
10. M. Rojas, O. Rojas, and S. M. de Souza, e-print arXiv: 1105.5130.
11. A. Ralko, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.84.184434 84, 184434 (2011).
12. K. S. Raman, R. Moessner, and S. L. Sondhi, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.72.064413 72, 064413 (2005). (Pubitemid 43292005)
13. E. Ressouche, V. Simonet, B. Canals, M. Gospodinov, and V. Skumryev, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.103.267204 103, 267204 (2009).
14. M. N. Iliev, A. P. Litvinchuk, V. G. Hadjiev, M. M. Gospodinov, V. Skumryev, and E. Ressouche, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.81. 024302 81, 024302 (2010).
15. R. Moessner and K. S. Raman, in Introduction to Frustrated Magnetism, edited by, C. Lacroix, P. Mendels, and, F. Mila, Springer Series in Solid-State Sciences, Vol. 164 (Springer, Berlin, 2011), Chap. 17.
16. Shamir, Acta Crystallogr. Sect. A ACACBN 0567-7394 10.1107/ S0567739478001412 34, 662 (1978).
17. A. K. Singh, Appl. Phys. Lett. APPLAB 0003-6951 10.1063/1.2905815 92, 132910 (2008). (Pubitemid 351483671)
18. S. Sachdev and R. N. Bhatt, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.41.9323 41, 9323 (1990).
19. J. Romhányi, K. Totsuka, and K. Penc, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.83.024413 83, 024413 (2011).
20. P. Chandra and B. Doucot, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.38.9335 38, 9335 (1988).
21. H. J. Schultz, T. A. L. Ziman, and D. Poilblanc, J. Phys. I JPGCE8 1155-4304 10.1051/jp1:1996236 6, 675 (1996).
22. R. F. Bishop, D. J. J. Farnell, and J. B. Parkinson, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.58.6394 58, 6394 (1998).
23. L. Capriotti, F. Becca, A. Parola, and S. Sorella, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.097201 87, 097201 (2001).
24. J. Sirker, Z. Weihong, O. P. Sushkov, and J. Oitmaa, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.73.184420 73, 184420 (2006). (Pubitemid 43748893)
25. R. Darradi, O. Derzhko, R. Zinke, J. Schulenburg, S. E. Krüger, and J. Richter, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.78.214415 78, 214415 (2008).
26. M. Roger, J. H. Hetherington, and J. M. Delrieu, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.55.1 55, 1 (1983).
27. P. Chandra, P. Coleman, and A. I. Larkin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.64.88 64, 88 (1990).
28. C. Weber, L. Capriotti, G. Misguich, F. Becca, M. Elhajal, and F. Mila, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.177202 91, 177202 (2003).
29. N. Shannon, T. Momoi, and P. Sindzingre, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.027213 96, 027213 (2006). (Pubitemid 43250685)
30. K. Penc and A. Läuchli, in Introduction to Frustrated Magnetism, edited by, C. Lacroix, P. Mendels, and, F. Mila, Springer Series in Solid-State Sciences, Vol. 164 (Springer, Berlin, 2011), Chap. 13.
31. A. Chubukov, E. Gagliano, and C. Balseiro, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.45.7889 45, 7889 (1992).
32. A. Läuchli, J. C. Domenge, C. Lhuillier, P. Sindzingre, and M. Troyer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.137206 95, 137206 (2005). (Pubitemid 41505590)
33. R. M. White, Quantum Theory of Magnetism, 3rd ed. (Springer-Verlag, Berlin, 2007), Chap. 8.
34. J.-P. Blaizot and G. Ripka, Quantum Theory of Finite Systems (MIT Press, Cambridge, MA, 1985), Chap. 3.
35. A. Jagannathan, R. Moessner, and S. Wessel, Phys. Rev. B 1098-0121 10.1103/PhysRevB.74.184410 74, 184410 (2006). (Pubitemid 44707980)
36. G. S. Uhrig, M. Holt, J. Oitmaa, O. P. Sushkov, and R. R. P. Singh, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.79.092416 79, 092416 (2009).
37. J. Alicea, A. V. Chubukov, and O. A. Starykh, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102.137201 102, 137201 (2009).
38. P. W. Anderson, Basic Notions of Condensed Matter Physics, Frontiers in Physics, Vol. 55 (Benjamin Cummings, London, 1984).
39. B. Bernu, C. Lhuillier, and L. Pierre, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.69.2590 69, 2590 (1992).
40. B. Bernu, P. Lecheminant, C. Lhuillier, and L. Pierre, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.50.10048 50, 10048 (1994).
41. P. Lecheminant, B. Bernu, C. Lhuillier, and L. Pierre, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.52.6647 52, 6647 (1995).
42. P. Lecheminant, B. Bernu, C. Lhuillier, L. Pierre, and P. Sindzingre, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.56.2521 56, 2521 (1997).
43. I. Rousochatzakis, A. M. Läuchli, and F. Mila, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.77.094420 77, 094420 (2008).
44. G. Misguich and P. Sindzingre, J. Phys. Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/19/14/145202 19, 145202 (2007). (Pubitemid 46491386)
45. S. K. Pati, R. R. P. Singh, and D. I. Khomskii, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81.5406 81, 5406 (1998).
46. P. Azaria, A. O. Gogolin, P. Lecheminant, and A. A. Nersesyan, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.624 83, 624 (1999).
47. C. Itoi, S. Qin, and I. Affleck, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.61.6747 61, 6747 (2000).
48. P. Azaria, E. Boulat, and P. Lecheminant, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.61.12112 61, 12112 (2000).
49. Y. Yamashita, N. Shibata, and K. Ueda, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.69.242 69, 242 (2000).
50. H. T. Ueda and K. Totsuka, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.76.214428 76, 214428 (2007).
51. P. Lecheminant and K. Totsuka, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.74.224426 74, 224426 (2006).
52. K. I. Kugel' and D. I. Khomskii, Sov. Phys. Usp. SOPUAP 0038-5670 10.1070/PU1982v025n04ABEH004537 25, 231 (1982).
53. O. Janson, I. Rousochatzakis, A. A. Tsirlin, J. Richter, Yu. Skourski, and H. Rosner, Phys. Rev. B 1098-0121 10.1103/PhysRevB.85.064404 85, 064404 (2012).
54. J. Oitmaa, C. Hamer, and W. Zheng, Series Expansion Methods for Strongly Interacting Lattice Models (Cambridge University Press, Cambridge, 2006).
55. D. J. Klein, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1682018 61, 786 (1974), Appendix A.
56. A. Läuchli, F. Mila, and K. Penc, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.087205 97, 087205 (2006). (Pubitemid 44277572)
57. B. A. Ivanov and A. K. Kolezhuk, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.68.052401 68, 052401 (2003).
58. M. Tinkham, Group Theory and Quantum Mechanics (Dover, New York, 2003).
59. M. El-Batanouny and F. Wooten, Symmetry and Condensed Matter Physics, A Computational Approach (Cambridge University Press, Cambridge, 2008).
60. T. Inui, Y. Tanabe, and Y. Onodera, Group Theory and Its Applications in Physics (Springer-Verlag, Berlin, 1996).
61. 33 in the limit of x → 0. Still, however, the up-down state is very different from a singlet wave function.