Tensor network decompositions in the presence of a global symmetry

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 82, Issue 5, 2010, Pages

  Singh, Sukhwinder ^a   Pfeifer, Robert N C ^a   Vidal, Guifré ^a  

^a UNIVERSITY OF QUEENSLAND   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL COSTS; DEGREES OF FREEDOM; GLOBAL SYMMETRIES; LATTICE SYSTEM; LOOP QUANTUM GRAVITY; MANY-BODY STATE; NETWORK ALGORITHMS; NETWORK DECOMPOSITION; NUMERICAL CALCULATION; NUMERICAL SIMULATION ALGORITHMS; QUANTUM GEOMETRY; SPIN NETWORKS; STRUCTURAL TENSORS; SYMMETRY GROUPS;

ALGORITHMS; COMPUTER SIMULATION; QUANTUM THEORY;

TENSORS;

EID: 78649568302     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.82.050301     Document Type: Review

References (24)

1. S. Ostlund and S. Rommer, Phys. Rev. Lett. 75, 3537 (1995)
2. M. Fannes, B. Nachtergaele, and R. Werner, Commun. Math. Phys. 144, 443 (1992).
3. F. Verstraete and J. I. Cirac, e-print arXiv:cond-mat/0407066v1
4. G. Sierra and M. A. Martin-Delgado, e-print arXiv:cond-mat/9811170v3.
5. G. Vidal, Phys. Rev. Lett. 99, 220405 (2007); 101, 110501 (2008).
6. G. Evenbly and G. Vidal, Phys. Rev. Lett. 104, 187203 (2010).
7. R. Penrose, Angular Momentum: An Approach to Combinatorial Space-time, 1971 [http://math.ucr.edu/home/baez/penrose/].
8. C. Rovelli and L. Smolin, Phys. Rev. D 52, 5743 (1995)
9. C. Rovelli, Living Rev. Relativity 11 (2008) [http://www.livingreviews.org/lrr-2008-5].
10. S. R. White, Phys. Rev. Lett. 69, 2863 (1992)
11. S. Ostlund and S. Rommer, Phys. Rev. Lett. 75, 3537 (1995)
12. G. Sierra and T. Nishino, Nucl. Phys. B 495, 505 (1997)
13. I. McCulloch and M. Gulacsi, Europhys. Lett. 57, 852 (2002)
14. I. McCulloch, J. Stat. Mech. (2007) P10014
15. S. Singh, H.-Q. Zhou, and G.Vidal, New J. Phys. 12, 033029 (2010)
16. D. Perez-Garcia et al., Phys. Rev. Lett. 100, 167202 (2008)
17. M. Sanz et al., Phys. Rev. A 79, 042308 (2009).
18. g.
19. J. F. Cornwell, Group Theory in Physics (Academic, New York, 1997).
20. ab.
21. See, for example, R. N. C. Pfeifer et al., Phys. Rev. B 82, 115126 (2010).
22. t need to be specified in Eq. (15), simplifying significantly the decomposition of symmetric tensors.
23. S. Singh, R. Pfeifer, and G. Vidal, e-print arXiv:1008.4774v1.
24. S. Singh and G. Vidal (unpublished).