Convex-set description of quantum phase transitions in the transverse Ising model using reduced-density-matrix theory

Journal of Chemical Physics

Volumn 130, Issue 22, 2009, Pages

  Schwerdtfeger, Christine A ^a   Mazziotti, David A ^a  

^a UNIVERSITY OF CHICAGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONVEX SET; CRITICAL FIELD STRENGTH; CRITICAL POINTS; EXACT SOLUTION; EXPECTATION VALUES; FINITE LATTICES; GROUND-STATE ENERGIES; HAMILTONIAN PARAMETERS; INFINITE LATTICES; LOWER BOUNDS; N-REPRESENTABILITY; ORDER PARAMETER; PAIR CORRELATION FUNCTIONS; PARTICLE SYSTEMS; PER UNIT; QUANTUM PHASE TRANSITIONS; QUANTUM PHASIS; QUANTUM SYSTEM; REDUCED-DENSITY MATRIX; REFERENCE WAVE FUNCTIONS; THERMODYNAMIC LIMITS; TRANSVERSE ISING MODELS; TRANSVERSE MAGNETIC FIELD;

CONTROL THEORY; ELECTRON TUNNELING; EQUATIONS OF STATE; GROUND STATE; ISING MODEL; MAGNETIC FIELDS; QUANTUM ELECTRONICS; QUANTUM OPTICS; SET THEORY; WAVE FUNCTIONS;

PHASE TRANSITIONS;

ARTICLE; CHEMICAL MODEL; COMPUTER SIMULATION; PHASE TRANSITION; QUANTUM THEORY;

COMPUTER SIMULATION; MODELS, CHEMICAL; PHASE TRANSITION; QUANTUM THEORY;

EID: 67449170295     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3143403     Document Type: Article

References (56)

1. S. Sachdev, Quantum Phase Transitions (Cambridge University Press, New York, 1999).
2. S. L. Sondhi, S. M. Girvin, J. P. Carini, and D. Shahar, Rev. Mod. Phys. 0034-6861 69, 315 (1997). 10.1103/RevModPhys.69.315
3. G. Gidofalvi and D. A. Mazziotti, Phys. Rev. A 1050-2947 74, 012501 (2006). 10.1103/PhysRevA.74.012501
4. Reduced-Density-Matrix Mechanics with Application to Many-Electron Atoms and Molecules, Advances in Chemical Physics Vol. 134, edited by, D. A. Mazziotti, (Wiley, New York, 2007).
5. A. J. Coleman and V. I. Yukalov, Reduced Density Matrices: Coulson's Challenge (Springer-Verlag, New York, 2000).
6. M. Rosina, in Many-Electron Densities and Reduced Density Matrices, edited by, J. Cioslowski, (Kluwer Academic, New York, 2000).
7. D. A. Mazziotti, Phys. Rev. A 1050-2947 65, 062511 (2002). 10.1103/PhysRevA.65.062511
8. R. M. Erdahl, Int. J. Quantum Chem. 0020-7608 13, 697 (1978). 10.1002/qua.560130603
9. J. E. Harriman, Phys. Rev. A 1050-2947 17, 1249 (1978). 10.1103/PhysRevA.17.1249
10. D. A. Mazziotti, Phys. Rev. A 1050-2947 57, 4219 (1998). 10.1103/PhysRevA.57.4219
11. S. Sachdev, Science 0036-8075 288, 475 (2000). 10.1126/science.288.5465. 475
12. S. Sachdev, Int. J. Mod. Phys. B 0217-9792 17, 5065 (2003). 10.1142/S021797920302020X
13. P. Pfeuty, Ann. Phys. 0003-3804 57, 79 (1970). 10.1016/0003-4916(70) 90270-8
14. B. M. McCoy, Phys. Rev. 0096-8250 173, 531 (1968). 10.1103/PhysRev.173. 531
15. E. Lieb, T. Schultz, and D. Mattis, Ann. Phys. 0003-3804 16, 407 (1961). 10.1016/0003-4916(61)90115-4
16. L. Sneddon and R. B. Stinchcombe, J. Phys. C 0022-3719 12, 3761 (1979). 10.1088/0022-3719/12/18/021
17. C. J. Hamer and M. Barber, J. Phys. A 0305-4470 13, L169 (1980). 10.1088/0305-4470/13/5/011
18. S. Katsura, Phys. Rev. 0096-8250 127, 1508 (1962). 10.1103/PhysRev.127. 1508
19. Y. Nonomura and M. Suzuki, J. Phys. A 0305-4470 25, 85 (1992). 10.1088/0305-4470/25/1/013
20. M. Campanino, A. Klein, and J. F. Perez, Commun. Math. Phys. 0010-3616 135, 499 (1991). 10.1007/BF02104118
21. A. Osterloh, L. Amico, G. Falci, and R. Fazio, Nature (London) 0028-0836 416, 608 (2002). 10.1038/416608a
22. G. R. Grimmett, T. J. Osborne, and P. F. Scudo, J. Stat. Phys. 0022-4715 131, 305 (2008). 10.1007/s10955-008-9502-6
23. L. F. Cugliandolo, G. S. Lozano, and H. F. Lozza, Int. J. Mod. Phys. B 0217-9792 20, 5219 (2006). 10.1142/S0217979206036296
24. J. Rodríguez-Laguna, J. Phys. A: Math. Theor. 1751-8113 40, 12043 (2007). 10.1088/1751-8113/40/40/003
25. Y. G. Wang, W. L. Zhong, and P. L. Zhang, Solid State Commun. 0038-1098 101, 807 (1997). 10.1016/S0038-1098(96)00730-2
26. Y. L. Wang and B. R. Cooper, Phys. Rev. 0096-8250 172, 539 (1968). 10.1103/PhysRev.172.539
27. W. P. Wolf, Braz. J. Phys. 0103-9733 30, 794 (2000). 10.1590/S0103- 97332000000400030
28. P. G. de Gennes, Solid State Commun. 0038-1098 1, 132 (1963). 10.1016/0038-1098(63)90212-6
29. J. H. Sebold and J. K. Percus, Mol. Phys. 0026-8976 86, 907 (1995). 10.1080/00268979500102481
30. F. Verstraete and J. I. Cirac, Phys. Rev. B 0163-1829 73, 094423 (2006). 10.1103/PhysRevB.73.094423
31. A. J. Coleman, Phys. Rev. A 1050-2947 66, 022503 (2002). 10.1103/PhysRevA.66.022503
32. R. M. Erdahl and B. Jin, in Many-Electron Densities and Density Matrices, edited by, J. Cioslowski, (Kluwer, Boston, 2000).
33. M. Nakata, H. Nakatsuji, M. Ehara, M. Fukuda, K. Nakata, and K. Fujisawa, J. Chem. Phys. 0021-9606 114, 8282 (2001). 10.1063/1.1360199
34. D. A. Mazziotti, Phys. Rev. Lett. 0031-9007 93, 213001 (2004). 10.1103/PhysRevLett.93.213001
35. D. A. Mazziotti, J. Chem. Phys. 0021-9606 121, 10957 (2004). 10.1063/1.1810134
36. Z. Zhao, B. J. Braams, H. Fukuda, M. L. Overton, and J. K. Percus, J. Chem. Phys. 0021-9606 120, 2095 (2004). 10.1063/1.1636721
37. E. Canc̀s, G. Stoltz, and M. Lewin, J. Chem. Phys. 0021-9606 125, 064101 (2006). 10.1063/1.2222358
38. D. A. Mazziotti, Acc. Chem. Res. 0001-4842 39, 207 (2006). 10.1021/ar050029d
39. D. A. Mazziotti, Phys. Rev. A 1050-2947 74, 032501 (2006). 10.1103/PhysRevA.74.032501
40. G. Gidofalvi and D. A. Mazziotti, J. Chem. Phys. 0021-9606 126, 024105 (2007). 10.1063/1.2423008
41. D. A. Mazziotti, Math. Modell. Numer. Anal. 0764-583X 41, 249 (2007). 10.1051/m2an:2007021
42. C. Garrod, V. Mihailović, and M. Rosina, J. Math. Phys. 0022-2488 16, 868 (1975). 10.1063/1.522634
43. D. A. Mazziotti and R. M. Erdahl, Phys. Rev. A 1050-2947 63, 042113 (2001). 10.1103/PhysRevA.63.042113
44. L. J. Kijewski and J. K. Percus, Phys. Rev. A 1050-2947 2, 1659 (1970). 10.1103/PhysRevA.2.1659
45. R. M. Erdahl, Rep. Math. Phys. 0034-4877 15, 147 (1979). 10.1016/0034-4877(79)90015-6
46. O. Derzhko, in Order, Disorder and Criticality, edited by, Y. Holovatch, (World Scientific, Singapore, 2004), Chap..
47. P. Surján, Second Quantized Approach to Quantum Chemistry (Springer-Verlag, New York, 1989).
48. N. Goldenfeld, Lectures on Phase Transitions and the Renormalization Group (Addison-Wesley, New York, 1992).
49. A. J. Coleman, Rev. Mod. Phys. 0034-6861 35, 668 (1963). 10.1103/RevModPhys.35.668
50. C. Garrod and J. Percus, J. Math. Phys. 0022-2488 5, 1756 (1964). 10.1063/1.1704098
51. A. J. Coleman, Int. J. Quantum Chem. 0020-7608 63, 23 (1997). 10.1002/(SICI)1097-461X(1997)63:1<23::AID-QUA5>3.0.CO;2-4
52. L. Vandenberghe and S. Boyd, SIAM Rev. 0036-1445 38, 49 (1996). 10.1137/1038003
53. Handbook of Semidefinite Programming-Theory, Algorithms, and Applications, edited by, H. Wolkowicz, R. Saigal, and, L. Vandenberghe, (Kluwer, Dordrecht, 2000).
54. S. Homer and M. Peinado, J. Parallel Distrib. Comput. 0743-7315 46, 48 (1997). 10.1006/jpdc.1997.1381
55. S. Burer and R. D. C. Monteiro, Math. Program. Ser. B 0025-5610 95, 329 (2003). 10.1007/s10107-002-0352-8
56. G. Gidofalvi and D. A. Mazziotti, Phys. Rev. A 1050-2947 72, 052505 (2005). 10.1103/PhysRevA.72.052505