Reducing memory cost of exact diagonalization using singular value decomposition

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 84, Issue 5, 2011, Pages

  Weinstein, Marvin ^a   Auerbach, Assa ^b,c   Chandra, V Ravi ^c  

^a SLAC NATIONAL ACCELERATOR LABORATORY   (United States)

^b STANFORD UNIVERSITY   (United States)

^c TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

ENTANGLEMENT ENTROPY; EXACT DIAGONALIZATION; HEISENBERG MODELS; LANCZOS ALGORITHM; LANCZOS VECTORS; LATTICE HAMILTONIANS; LATTICE SYMMETRY; MEMORY COST; REDUCED MEMORY REQUIREMENTS; SUB-CLUSTERS; TRUNCATION ERRORS;

ALGORITHMS; CRYSTAL LATTICES; HAMILTONIANS; QUANTUM ENTANGLEMENT;

SINGULAR VALUE DECOMPOSITION;

EID: 81555195700     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.84.056701     Document Type: Article

References (31)

1. C. J. Morningstar and M. Weinstein, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.54.4131 54, 4131 (1996);
2. M. Weinstein, Phys. Rev. B 1098-0121 10.1103/PhysRevB.63.174421 63, 174421 (2001);
3. M. Stewart Siu and M. Weinstein, Phys. Rev. B PRVDAQ 1098-0121 10.1103/PhysRevB.75.184403 75, 184403 (2007).
4. E. Altman and A. Auerbach, Phys. Rev. B PRVDAQ 1098-0121 10.1103/PhysRevB.65.104508 65, 104508 (2002);
5. E. Berg, E. Altman, and A. Auerbach, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.147204 90, 147204 (2003);
6. R. Budnik and A. Auerbach, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.187205 93, 187205 (2004).
7. S. Capponi, A. Läuchli, and M. Mambrini, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.70.104424 70, 104424 (2004).
8. For recent advances in ED on large Kagomé clusters see A. M. Läuchli, J. Sudan, E. S. Sorensen, Phys. Rev. B 10.1103/PhysRevB.83.212401 83, 212401 (2011)
9. N. H. Lindner and A. Auerbach, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.81.054512 81, 054512 (2010).
10. J. E. Avron and R. Seiler, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.54.259 54, 259 (1985);
11. N. Lindner, A. Auerbach, and D. P. Arovas, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.82.134510 82, 134510 (2010).
12. C. Lanczos, J. Res. Natl. Bur. Stand. 45, 255 (1950).
13. J. K. Cullum and R. A. Willoughby, Lanczos Algorithms for Large Symmetric Eigenvalue Computations, (Birkhäuser, Boston, 1985).
14. L. Amico, R. Fazio, A. Osterloh, and V. Vedral, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.80.517 80, 517 (2008), and references therein. (Pubitemid 351697445)
15. F. Verstraete, M. A. Martin-Delgado, and J. I. Cirac, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.087201 92, 087201 (2004).
16. M. B. Hastings, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.69.104431 69, 104431 (2004).
17. E. Fradkin and J. E. Moore, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.050404 97, 050404 (2006). (Pubitemid 44188134)
18. I. Klich, G. Refael, and A. Silva, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.74.032306 74, 032306 (2006). (Pubitemid 44373648)
19. S. R. White, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.69. 2863 69, 2863 (1992);
20. S. R. White, Phys. Rev. Lett. PRLTAO 1098-0121 10.1103/PhysRevB.48.10345 48, 10345 (1993).
21. S. Ostlund and S. Rommer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.75.3537 75, 3537 (1995).
22. T. Papenbrock and D. J. Dean, Phys. Rev. C PRVCAN 0556-2813 10.1103/PhysRevC.67.051303 67, 051303 (2003).
23. G. Vidal, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.220405 99, 220405 (2007); (Pubitemid 350191565)
24. L. Tagliacozzo, G. Evenbly, and G. Vidal, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.80.235127 80, 235127 (2009);
25. G. Evenbly and G. Vidal, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.104.187203 104, 187203 (2010).
26. A power law can fit the numerical entanglement spectra asymptotics of two dimensional systems computed by, e.g., M-C. Chung and I. Peschel, Phys. Rev. B PRLTAO 1098-0121 10.1103/PhysRevB.64.064412 64, 064412 (2001);
27. H. Li and F. D. M. Haldane, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.101.010504 101, 010504 (2008).
28. M. Weinstein, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.47.5499 47, 5499 (1993).
29. S. Capponi (private communication).
30. E. M. Stoudenmire and Steven R. White, e-print arXiv: 1105.1374.
31. A. Auerbach, S. Capponi, V. Ravi Chandra, and M. Weinstein (unpublished).