Heisenberg antiferromagnet on Cayley trees: Low-energy spectrum and even/odd site imbalance

Physical Review B - Condensed Matter and Materials Physics

Volumn 87, Issue 8, 2013, Pages

  Changlani, Hitesh J ^a   Ghosh, Shivam ^a   Henley, Christopher L ^a   Läuchli, Andreas M ^b  

^a Laboratory of Atomic and Solid State Physics and Sibley School of Mechanical and Aerospace Engineering   (United States)

^b UNIVERSITY OF INNSBRUCK   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84874516838     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.87.085107     Document Type: Article

References (59)

1. M. Takahashi, Prog. Theor. Phys. Suppl. PTPSAL 0375-9687 10.1143/PTPS.87.233 87, 233 (1986);
2. M. Takahashi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.58. 168 58, 168 (1987).
3. J. E. Hirsch and S. Tang, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.40.4769 40, 4769 (1989).
4. E. Manousakis, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.63.1 63, 1 (1991).
5. S. Sarker, C. Jayaprakash, H. R. Krishnamurthy, and M. Ma, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.40.5028 40, 5028 (1989).
6. A. Auerbach and D. P. Arovas, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.61.617 61, 617 (1988);
7. D. P. Arovas and A. Auerbach, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.38.316 38, 316 (1988).
8. A. Auerbach and D. P. Arovas, arXiv: 0809.4836.
9. A. V. Chubukov, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.44.12318 44, 12318 (1991).
10. A. V. Chubukov, S. Sachdev, and J. Ye, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.49.11919 49, 11919 (1994).
11. N. Trivedi and D. M. Ceperley, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.41.4552 41, 4552 (1990).
12. K. H. Hoglund and A. W. Sandvik, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.79.020405 79, 020405 (2009).
13. M. A. Metlitski and S. Sachdev, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.78.174410 78, 174410 (2008).
14. A. L. Chernyshev, Y. C. Chen, and A. H. Castro Neto, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.067209 87, 067209 (2001).
15. In the literature, the "Bethe lattice" is often used to refer to the thermodynamic limit of the "Cayley tree," where the effect of boundaries is eliminated [see for example Laumann (Ref.) which considers random graphs of fixed connectivity]. For the purpose of this paper, the presence of open boundaries will play an important role in the low-energy physics and so we will simply use the term "Cayley tree."
16. P. W. Anderson, Phys. Rev. 0031-899X 10.1103/PhysRev.86.694 86, 694 (1952);
17. P. W. Anderson, Basic Notions of Condensed Matter Physics (Benjamin, New York, 1984), Sec. 2D, pp. 44-46.
18. C. Lhuillier, arXiv: cond-mat/0502464.
19. Subir Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, UK, 1999).
20. H. Neuberger and T. Ziman, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.39.2608 39, 2608 (1989).
21. M. Gross, E. Sanchez-Velasco, and E. Siggia, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.39.2484 39, 2484 (1989).
22. L. Wang and A. W. Sandvik, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.117204 97, 117204 (2006); (Pubitemid 44396681)
23. L. Wang and A. W. Sandvik, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.81.054417 81, 054417 (2010).
24. H. Otsuka, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.53.14004 53, 14004 (1996).
25. B. Friedman, J. Phys.: Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/9/42/016 9, 9021 (1997).
26. M. Kumar, S. Ramasesha, and Z. G. Soos, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.85.134415 85, 134415 (2012).
27. C. R. Laumann, S. A. Parameswaran, and S. L. Sondhi, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.80.144415 80, 144415 (2009).
28. G. Semerjian, M. Tarzia, and F. Zamponi, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.80.014524 80, 014524 (2009).
29. W. F. Brinkman and T. M. Rice, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.2.1324 2, 1324 (1970).
30. A. Georges, G. Kotliar, W. Krauth, and M. J. Rozenberg, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.68.13 68, 13 (1996).
31. M. A. Martin-Delgado, J. Rodriguez-Laguna, and G. Sierra, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.65.155116 65, 155116 (2002).
32. D. Astruc, E. Boisselier, and C. Ornelas, Chem. Rev. CHREAY 0009-2665 10.1021/cr900327d 110, 1857 (2010).
33. M. Takahata, M. Shoji, H. Nitta, R. Takeda, S. Yamanaka, M. Okumura, M. Nakano, and K. Yamaguchi, Int. J. Quantum Chem. IJQCB2 0020-7608 10.1002/qua.20801 105, 615 (2005). (Pubitemid 43082099)
34. S. R. White, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.69. 2863 69, 2863 (1992);
35. S. R. White, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.48.10345 48, 10345 (1993).
36. W. Münder, A. Weichselbaum, A. Holzner, J. von Delft, and C. L. Henley, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/12/7/075027 12, 075027 (2010).
37. W. Marshall, Proc. R. Soc. London A 1364-5021 10.1098/rspa.1955.0200 232, 48 (1955);
38. E. H. Lieb and D. Mattis, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1724276 3, 749 (1962);
39. M. B. Hastings, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.69.104431 69, 104431 (2004).
40. K. G. Wilson, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.47.773 47, 773 (1975).
41. M. B. Lepetit, M. Cousy, and G. M. Pastor, Eur. Phys. J. B EPJBFY 1434-6028 10.1007/s100510050053 13, 3 (2000).
42. V. Murg, F. Verstraete, Ö. Legeza, R. M. Noack, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.82.205105 82, 205105 (2010).
43. H. J. Changlani, S. Ghosh, S. Pujari, and C. L. Henley, arXiv: 1210.4621.
44. Z. Bai, J. Demmel, J. Dongarra, A. Ruhe, and H. van der Vorst (eds.), Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide (SIAM, Philadelphia, PA, 2000).
45. R. P. Feynman, Statistical Mechanics (Benjamin, New York, 1972).
46. j 〈 S z tot S j z ⌠which equals zero for a state with S z tot = 0.
47. C. R. Laumann, S. A. Parameswaran, S. L. Sondhi, and F. Zamponi, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.81.174204 81, 174204 (2010).
48. S. Sachdev, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.45.12377 45, 12377 (1992).
49. G. Misguich, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.86.245132 86, 245132 (2012).
50. L. Messio, O. Cepas, and C. Lhuillier, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.81.064428 81, 064428 (2010).
51. See, for example, E. R. Mucciolo, A. H. Castro Neto, and Claudio Chamon, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.69.214424 69, 214424 (2004).
52. A. Auerbach, Interacting Electrons and Quantum Magnetism (Springer-Verlag, New York, NY, 1994).
53. T. Tay and O. I. Motrunich, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.84.020404 84, 020404 (R) (2011).
54. P. Chandra and B. Doucot, J. Phys. A 1361-6447 10.1088/0305-4470/27/5/019 27, 1541 (1994).
55. H. J. Changlani, R. Lamberty, and C. L. Henley (unpublished).
56. L. Messio, B. Bernu, and C. Lhuillier, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.108.207204 108, 207204 (2012).
57. X. G. Wen, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.65.165113 65, 165113 (2002).
58. F. Wang, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.82.024419 82, 024419 (2010);
59. F. Wang and A. Vishwanath, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.74.174423 74, 174423 (2006). (Pubitemid 44791132)