Quantum phases of the planar antiferromagnetic J1-J 2-J3 Heisenberg model

Physical Review B - Condensed Matter and Materials Physics

Volumn 83, Issue 6, 2011, Pages

  Reuther, Johannes ^a   Wölfle, Peter ^a   Darradi, Rachid ^b   Brenig, Wolfram ^b   Arlego, Marcelo ^c   Richter, Johannes ^d  

^a KARLSRUHE INSTITUTE OF TECHNOLOGY   (Germany)

^b TECHNICAL UNIVERSITY OF BRAUNSCHWEIG   (Germany)

^c UNIVERSIDAD NACIONAL DE LA PLATA   (Argentina)

^d OTTO VON GUERICKE UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79961050804     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.83.064416     Document Type: Article

References (55)

1. P. Chandra and B. Doucot, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.38.9335 38, 9335 (1988).
2. H. J. Schulz and T. A. L. Ziman, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/18/4/013 18, 355 (1992).
3. J. Richter and J. Schulenburg, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2009-00400-4 73, 117 (2010).
4. N. Read and S. Sachdev, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.62.1694 62, 1694 (1989).
5. M. E. Zhitomirsky and K. Ueda, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.54.9007 54, 9007 (1996).
6. L. Capriotti, F. Becca, A. Parola, and S. Sorella, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.097201 87, 097201 (2001).
7. T. Senthil, A. Vishwanath, L. Balents, S. Sachdev, and M. P. A. Fisher, Science SCIEAS 0036-8075 10.1126/science.1091806 303, 1490 (2004). (Pubitemid 38314412)
8. R. Darradi, O. Derzhko, R. Zinke, J. Schulenburg, S. E. Krüger, and J. Richter, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.78.214415 78, 214415 (2008).
9. R. Melzi, P. Carretta, A. Lascialfari, M. Mambrini, M. Troyer, P. Millet, and F. Mila, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.1318 85, 1318 (2000);
10. P. Carretta, R. Melzi, N. Papinutto, and P. Millet, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.047601 88, 047601 (2002);
11. H. Rosner, R. R. P. Singh, W. H. Zheng, J. Oitmaa, S.-L. Drechsler, and W. E. Pickett, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.186405 88, 186405 (2002);
12. A. Bombardi, J. Rodriguez-Carvajal, S. Di Matteo, F. de Bergevin, L. Paolasini, P. Carretta, P. Millet, and R. Caciuffo, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.027202 93, 027202 (2004).
13. P. Carretta, N. Papinutto, C. B. Azzoni, M. C. Mozzati, E. Pavarini, S. Gonthier, and P. Millet, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.66. 094420 66, 094420 (2002).
14. R. Nath, A. A. Tsirlin, H. Rosner, and C. Geibel, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.78.064422 78, 064422 (2008).
15. A. Moreo, E. Dagotto, T. Jolicoeur, and J. Riera, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.42.6283 42, 6283 (1990).
16. A. Chubukov, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.44.392 44, 392 (1991).
17. E. Rastelli and A. Tassi, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.46.10793 46, 10793 (1992).
18. J. Ferrer, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.47.8769 47, 8769 (1993).
19. H. A. Ceccatto, C. J. Gazza, and A. E. Trumper, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.47.12329 47, 12329 (1993).
20. P. W. Leung and N. W. Lam, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.53.2213 53, 2213 (1996).
21. L. Capriotti and S. Sachdev, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.257206 93, 257206 (2004). (Pubitemid 40121255)
22. M. Mambrini, A. Lauechli, D. Poilblanc, and F. Mila, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.74.144422 74, 144422 (2006). (Pubitemid 44631176)
23. M. Arlego and W. Brenig, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.78.224415 78, 224415 (2008).
24. V. Murg, F. Verstraete, and J. I. Cirac, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.79.195119 79, 195119 (2009).
25. A. Ralko, M. Mambrini, and D. Poilblanc, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.80.184427 80, 184427 (2009).
26. P. Sindzingre, N. Shannon, and T. Momoi, J. Phys.: Conf. Ser. PRLTAO 1742-6588 10.1088/1742-6596/200/2/022058 200, 022058 (2010).
27. M. Salmhofer and C. Honerkamp, Prog. Theor. Phys. PTPKAV 0033-068X 10.1143/PTP.105.1 105, 1 (2001).
28. J. Reuther and P. Wölfle, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.81.144410 81, 144410 (2010).
29. J. Reuther and R. Thomale, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.83.024402 83, 024402 (2011).
30. A. A. Katanin, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.70.115109 70, 115109 (2004).
31. M. Salmhofer, C. Honerkamp, W. Metzner, and O. Lauscher, Prog. Theor. Phys. PTPKAV 0033-068X 10.1143/PTP.112.943 112, 943 (2004). (Pubitemid 40366574)
32. C. Zeng, D. J. J. Farnell, and R. F. Bishop, J. Stat. Phys. JSTPBS 0022-4715 10.1023/A:1023220222019 90, 327 (1998).
33. S. E. Krüger and J. Richter, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.64.024433 64, 024433 (2001).
34. R. F. Bishop, D. J. J. Farnell, S. E. Krüger, J. B. Parkinson, and J. Richter, J. Phys. Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/12/30/ 316 12, 6877 (2000).
35. D. J. J. Farnell and R. F. Bishop, in Quantum Magnetism, edited by, U. Schollwöck, J. Richter, D. J. J. Farnell, and, R. F. Bishop, Lecture Notes in Physics Vol. 645 (Springer, Berlin, 2004), p. 307.
36. R. Darradi, J. Richter, and D. J. J. Farnell, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.72.104425 72, 104425 (2005). (Pubitemid 43022395)
37. D. Schmalfuß, R. Darradi, J. Richter, J. Schulenburg, and D. Ihle, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.157201 97, 157201 (2006). (Pubitemid 44547768)
38. R. F. Bishop, P. H. Y. Li, R. Darradi, and J. Richter, J. Phys. Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/20/25/255251 20, 255251 (2008). (Pubitemid 351777644)
39. R. F. Bishop, P. H. Y. Li, R. Darradi, J. Schulenburg, and J. Richter, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.78.054412 78, 054412 (2008).
40. R. Zinke, J. Schulenburg, and J. Richter, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2008-00055-7 64, 147 (2008).
41. J. Richter, R. Darradi, J. Schulenburg, D. J. J. Farnell, and H. Rosner, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.81.174429 81, 174429 (2010).
42. R. Bursill, G. A. Gehring, D. J. J. Farnell, J. B. Parkinson, T. Xiang, and C. Zeng, J. Phys. Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/7/45/ 016 7, 8605 (1995).
43. R. F. Bishop, P. H. Y. Li, D. J. J. Farnell, and C. E. Campbell, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.79.174405 79, 174405 (2009).
44. R. Zinke, S.-L. Drechsler, and J. Richter, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.79.094425 79, 094425 (2009).
45. F. J. Wegner, Ann. Phys. ANPYA2 0003-3804 10.1002/andp.19945060203 3, 77 (1994).
46. C. Knetter and G. S. Uhrig, Eur. Phys. J. B EPJBFY 1434-6028 10.1007/s100510050026 13, 209 (2000).
47. M. Arlego and W. Brenig, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.75.024409 75, 024409 (2007).
48. M. Arlego and W. Brenig, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2006-00366-7 53, 193 (2006). (Pubitemid 44596143)
49. W. Brenig and M. Grzeschik, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.69.064420 69, 064420 (2004).
50. W. Brenig, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.67.064402 67, 064402 (2003).
51. W. Brenig and A. Honecker, Phys. Rev. B PLRBAQ 1098-0121 10.1103/PhysRevB.65.140407 65, 140407 (R) (2002).
52. R. Hedden, V. Meden, T. Pruschke, and K. Schönhammer, J. Phys. Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/16/29/019 16, 5279 (2004).
53. 0 will be made available by email from the authors upon request.
54. Figure 3 displays PEPS with local dimension D = 4. The improvement over D = 3 (see Ref. 21) is small on the y scale of Fig. 3. This may suggest rather large values of D to be necessary to improve PEPS.
55. J.-K. Kim and M. Troyer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80.2705 80, 2705 (1998).