Efficient simulation of one-dimensional quantum many-body systems

Physical Review Letters

Volumn 93, Issue 4, 2004, Pages

  Vidal, Guifré ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL METHODS; COMPUTER SIMULATION; DYNAMICS; GROUND STATE; HAMILTONIANS; ITERATIVE METHODS; MATRIX ALGEBRA; PERTURBATION TECHNIQUES;

DENSITY MATRIX RENORMALIZATION GROUP (DMRG); LOW-ENERGY DYNAMICS; QUANTUM MANY-BODY SYSTEMS; QUANTUM SPIN CHAINS;

QUANTUM THEORY;

EID: 4344570203     PISSN: 00319007     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevLett.93.040502     Document Type: Article

References (31)

1. See, for instance, S. Albeverio, F. Gesztesy, R. Hoegh-Krohn, and H. Holden, Solvable Models in Quantum Mechanics, Texts and Monographs in Physics (Springer-Verlag, New York, 1988) ; A. G. Ushveridze, Quasi-Exactly Solvable Models in Quantum Mechanics (Institute of Physics Publishing, London, 1994).
2. See, for instance, S. Albeverio, F. Gesztesy, R. Hoegh-Krohn, and H. Holden, Solvable Models in Quantum Mechanics, Texts and Monographs in Physics (Springer-Verlag, New York, 1988) ; A. G. Ushveridze, Quasi-Exactly Solvable Models in Quantum Mechanics (Institute of Physics Publishing, London, 1994).
3. M. Suzuki, Quantum Monte Carlo Methods in Equilibrium and Nonequilibrium Systems, Springer Series in Solid-State Sciences (Springer-Verlag, Berlin, 1986).
4. S. R. White, Phys. Rev. B 48, 10345 (1993) ; S. Rommer and S. Östlund, Density Matrix Renormalization (Springer-Verlag, Berlin, 1999).
5. S. R. White, Phys. Rev. B 48, 10345 (1993) ; S. Rommer and S. Östlund, Density Matrix Renormalization (Springer-Verlag, Berlin, 1999).
6. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, England, 2000).
7. G. Vidal, Phys. Rev. Lett. 91, 147902 (2003).
8. J. Preskill, J. Mod Opt. 47, 127 (2000).
9. G. Vidai, J. I. Latorre, E. Rico, and A. Kitaev, Phys. Rev. Lett. 90, 227902 (2003).
10. H. L. Haselgrove, M. A. Nielsen, and T. J. Osborne, quant-ph/0308083.
11. F. Verstraete, M. Popp, and J. I. Cirac, quant-ph/0307009.
12. The definition of χ in the present work, Eq. (3), differs from that of Eq. (3) in [5]. In the latter the maximization of χ A considered all possible blocks A and not just those containing the m first systems. Therefore the condition that χ be small is here significantly less demanding, as a restriction on entanglement, than the analogous condition in [5].
13. n that is a sum of terms, each one involving at most k systems, for a small k independent of n. Physically reasonable Hamiltonians are of this form However, Hamiltonian (4) contains some additional constraints.
14. M. Fannes, B. Nachtergaele, and R. F. Werner, Commun. Math. Phys. 144, 443 (1992) ; J. Funct. Anal. 120, 511 (1994).
15. M. Fannes, B. Nachtergaele, and R. F. Werner, Commun. Math. Phys. 144, 443 (1992) ; J. Funct. Anal. 120, 511 (1994).
16. I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Phys. Rev. Lett. 59, 799 (1987) ; Commun. Math. Phys. 155, 477 (1988).
17. I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Phys. Rev. Lett. 59, 799 (1987) ; Commun. Math. Phys. 155, 477 (1988).
18. S. Östlund and S. Rommer, Phys. Rev. Lett. 75, 3537 (1995).
19. See A. J. Daley, C. Kollath, U. Schollwoeck, and G. Vidal, J. Stat. Mech. P04005 (2004), http://www.iop.org/EJ/abstract/1742-5468/2004/04/P04005, for a comparison between DMRG and the present simulation algorithm.
20. E. Schmidt, Math. Ann. 63, 433 (1907) ; A. Ekert and P. L. Knight, Am. J. Phys. 63, 415 (1995) ; A. Peres, Quantum Theory: Concepts and Methods (Kluwer Academic Publishers, Dordrecht, 1995).
21. E. Schmidt, Math. Ann. 63, 433 (1907) ; A. Ekert and P. L. Knight, Am. J. Phys. 63, 415 (1995) ; A. Peres, Quantum Theory: Concepts and Methods (Kluwer Academic Publishers, Dordrecht, 1995).
22. E. Schmidt, Math. Ann. 63, 433 (1907) ; A. Ekert and P. L. Knight, Am. J. Phys. 63, 415 (1995) ; A. Peres, Quantum Theory: Concepts and Methods (Kluwer Academic Publishers, Dordrecht, 1995).
23. The conditions under which such an exponential decay occurs are presently under investigation.
24. See I. Peschel, J. Phys. A 36, L205 (2003), and references therein.
25. y)/2 acting on several sites of a spin chain, or a product of (real space) creation operators a† in a 1D bosonic or fermionic system.
26. n is approximately constant between t and t + ΔT, and to each interval we apply the same reasoning as in the time-independent case.
27. M. Suzuki, Phys. Lett. A 146, 319 (1990) ; J. Math. Phys. (N.Y.) 32, 400 (1991). For third and fourth order expansions, see also A. T. Sornborger and E. D. Stewart, quant-ph/9809009.
28. M. Suzuki, Phys. Lett. A 146, 319 (1990) ; J. Math. Phys. (N.Y.) 32, 400 (1991). For third and fourth order expansions, see also A. T. Sornborger and E. D. Stewart, quant-ph/9809009.
29. M. Suzuki, Phys. Lett. A 146, 319 (1990) ; J. Math. Phys. (N.Y.) 32, 400 (1991). For third and fourth order expansions, see also A. T. Sornborger and E. D. Stewart, quant-ph/9809009.
30. 2.
31. -10.