Stability of the U(1) spin liquid with a spinon Fermi surface in 2+1 dimensions

Physical Review B - Condensed Matter and Materials Physics

Volumn 78, Issue 8, 2008, Pages

  Lee, Sung Sik ^a  

^a MCMASTER UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 50449102225     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.78.085129     Document Type: Article

References (45)

1. F. D. M. Haldane, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/14/19/010 14, 2585 (1981).
2. R. B. Laughlin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.50. 1395 50, 1395 (1983).
3. P. W. Anderson, Science SCIEAS 0036-8075 10.1126/science.235.4793.1196 235, 1196 (1987)
4. P. Fazekas and P. W. Anderson, Philos. Mag. PHMAA4 0031-8086 10.1080/14786439808206568 30, 423 (1974).
5. P. A. Lee, N. Nagaosa, and X.-G. Wen, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.78.17 78, 17 (2006), and references therein.
6. X.-G. Wen, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.65.165113 65, 165113 (2002).
7. M. A. Levin and X.-G. Wen, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.67.245316 67, 245316 (2003)
8. M. A. Levin and X.-G. Wen, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.71.045110 71, 045110 (2005)
9. M. A. Levin and X.-G. Wen, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.77.871 77, 871 (2005).
10. S.-S. Lee and P. A. Lee, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.72.235104 72, 235104 (2005).
11. T. Senthil and P. A. Lee, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.71.174515 71, 174515 (2005).
12. Y. Shimizu, K. Miyagawa, K. Kanoda, M. Maesato, and G. Saito, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.107001 91, 107001 (2003).
13. J. S. Helton, K. Matan, M. P. Shores, E. A. Nytko, B. M. Bartlett, Y. Yoshida, Y. Takano, A. Suslov, Y. Qiu, J.-H. Chung, D. G. Nocera, and Y. S. Lee, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.107204 98, 107204 (2007).
14. O. I. Motrunich, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.72.045105 72, 045105 (2005).
15. S.-S. Lee and P. A. Lee, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.036403 95, 036403 (2005).
16. Y. Ran, M. Hermele, P. A. Lee, and X.-G. Wen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.117205 98, 117205 (2007).
17. T. Senthil, M. Vojta, and S. Sachdev, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.69.035111 69, 035111 (2004).
18. O. I. Motrunich and M. P. A. Fisher, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.75.235116 75, 235116 (2007).
19. W. Rantner and X.-G. Wen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.3871 86, 3871 (2001)
20. W. Rantner and X.-G. Wen, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.66.144501 66, 144501 (2002).
21. P. A. Lee and N. Nagaosa, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.46.5621 46, 5621 (1992).
22. B. I. Halperin, P. A. Lee, and N. Read, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.47.7312 47, 7312 (1993).
23. J. Polchinski, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(94)90449- 9 422, 617 (1994).
24. Y. B. Kim, A. Furusaki, X.-G. Wen, and P. A. Lee, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.50.17917 50, 17917 (1994).
25. B. L. Altshuler, L. B. Ioffe, and A. J. Millis, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.50.14048 50, 14048 (1994).
26. A. M. Polyakov, Phys. Lett. PYLBAJ 0370-2693 10.1016/0370-2693(75)90162-8 59B, 82 (1975)
27. A. M. Polyakov, Nucl. Phys. B NUPBBO 0550-3213 10.1016/0550-3213(77) 90086-4 120, 429 (1977).
28. M. Hermele, T. Senthil, M. P. A. Fisher, P. A. Lee, N. Nagaosa, and X.-G. Wen, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.70.214437 70, 214437 (2004).
29. L. B. Ioffe and A. I. Larkin, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.39.8988 39, 8988 (1989).
30. N. Nagaosa, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.71.4210 71, 4210 (1993).
31. I. Ichinose, T. Matsui, and M. Onoda, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.64.104516 64, 104516 (2001).
32. I. F. Herbut, B. H. Seradjeh, S. Sachdev, and G. Murthy, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.68.195110 68, 195110 (2003).
33. K.-S. Kim, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.72.245106 72, 245106 (2005).
34. R. K. Kaul, S. Sachdev, and C. Xu, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.78.045110 78, 045110 (2008).
35. R. Shankar, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.66.129 66, 129 (1994).
36. The fact that the twist angles saturate to π only in the large L limit is due to the nonlocal nature of the instanton operator.
37. It is convenient to choose the temporal gauge for the singular part and the Coulomb gauge for the nonsingular part. Note that it is possible to choose different gauges for singular and nonsingular parts.
38. F. D. M. Haldane, in Perspectives in Many-Particle Physics, edited by, R. Broglia, and, J. R. Schrieffer, (North-Holland, Amsterdam, 1994).
39. A. Houghton and J. B. Marston, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.48.7790 48, 7790 (1993).
40. A. H. Castro Neto and E. Fradkin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.72.1393 72, 1393 (1994).
41. H.-J. Kwon, A. Houghton, and J. B. Marston, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.73.284 73, 284 (1994).
42. S.-S. Lee, P. A. Lee, and T. Senthil, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.067006 98, 067006 (2007).
43. V. Galitski and Y. B. Kim, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.266403 99, 266403 (2007).
44. S. Sachdev (private communication).
45. For example, see J. Polchinski, String Theory (Cambridge University Press, Cambridge, England, 1998), Vol. II, Chap..