Density matrix renormalization group in a two-dimensional λΦ4 hamiltonian lattice model

Journal of High Energy Physics

Volumn 8, Issue 5, 2004, Pages 139-154

  Sugihara, Takanori ^a  

^a RIKEN BNL RESEARCH CENTER   (United States)

Author keywords

Field Theories in Lower Dimensions; Lattice Gauge Field Theories; Renormalization Group; Spontaneous Symmetry Breaking

Indexed keywords

EID: 23044432573     PISSN: 10298479     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (31)

1. H. Bethe, On the theory of metals, 1. Eigenvalues and eigenfunctions for the linear atomic chain, Z. Phys. 71 (1931) 205-226.
2. C.-N. Yang, Some exact results for the many body problems in one dimension with repulsive delta function interaction, Phys. Rev. Lett. 19 (1967) 1312.
3. f on the light cone, Phys. Rev. D 49 (1994) 4226 [hep-th/9309128].
4. T. Sugihara, M. Matsuzaki and M. Yahiro, Two-dimensional SU(N) gauge theory on the light cone, Phys. Rev. D 50 (1994) 5274 [hep-th/9402092].
5. T. Sugihara, Variational calculation of the effective action, Phys. Rev. D 57 (1998) 7373 [hep-th/9711129].
6. T. Sugihara and M.-A. Taniguchi, Manifestation of a nontrivial vacuum in discrete light-cone quantization, Phys. Rev. Lett. 87 (2001) 271601 [hep-th/0104012].
7. T. Sugihara, Basis optimization renormalization group for quantum hamiltonian, Nucl. Phys. 108 (Proc. Suppl.) (2002) 267 [hep-th/0104013].
8. N. Sakai and M. Sakamoto, Lattice supersymmetry and the Nicolai mapping, Nucl. Phys. B 229 (1983) 173.
9. P. Fendley, K. Schoutens and J. de Boer, Lattice models with N = 2 supersymmetry, Phys. Rev. Lett. 90 (2003) 120402 [hep-th/0210161].
10. K.G. Wilson, The renormalization group: critical phenomena and the kondo problem, Rev. Mod. Phys. 47 (1975) 773.
11. S.R. White, Density matrix formulation for quantum renormalization groups, Phys. Rev. Lett. 69 (1992) 2863.
12. S.R. White, Density-matrix algorithms for quantum renormalization groups, Phys. Rev. B 48 (1993) 10345.
13. T. Xiang, Density-matrix renormalization-group method in momentum space, Phys. Rev. B 53 (1996) R10445.
14. T. Xiang, J. Lou and Z. Su, Two-dimensional algorithm of the density-matrix renormalization group, Phys. Rev. B 64 (2001) 104414.
15. R.J. Bursill, T. Xiang and G.A. Gehring, The density matrix renormalization group for a quantum spin chain at non-zero temperature, J. Phys.: Condens. Matter 8 (1996) L583.
16. X. Wang and T. Xiang, Transfer-matrix density-matrix renormalization- group theory for thermodynamics of one-dimensional quantum systems, Phys. Rev. B 56 (1997) 5061.
17. T. Xiang, Thermodynamics of quantum Heisenberg spin chains, Phys. Rev. B 58 (1998) 9142.
18. N. Shibata, Thermodynamics of the anisotropic Heisenberg chain calculated by the density matrix renormalization group method, J. Phys. Soc. Jpn. 66 (1997) 2221.
19. I. Peschel, X. Wang, M. Kaulke and K. Hallberg (Eds.), Density-matrix renormalization: a new numerical method in physics, Springer-Verlag, Berlin 1999.
20. T. Byrnes, P. Sriganesh, R.J. Bursill and C.J. Hamer, Density matrix renormalisation group approach to the massive schwinger model, Phys. Rev. D 66 (2002) 013002 [hep-lat/0202014].
21. J.B. Kogut and L. Susskind, Hamiltonian formulation of Wilson's lattice gauge theories, Phys. Rev. D 11 (1975) 395.
22. 4, Phys. Rev. D 58 (1998) 076003 [hep-lat/9712008].
23. L. Onsager, Crystal statistics. I. a two-dimensional model with an order-disorder transition, Phys. Rev. 65 (1944) 117.
24. T. Sugihara, Lattice chiral symmetry with nonlocal interactions, Phys. Rev. D 68 (2003) 034502 [hep-lat/0304015].
25. T. Sugihara, Vector and chiral gauge theories on the lattice, hep-lat/0310061.
26. 4 field theory, Phys. Rev. D 13 (1976) 2778, erratum ibid. D16 (1976) 1979.
27. 4 quantum field theory with postgaussian approximations, Phys. Rev. D 35 (1987) 621.
28. 4 theory by discretized light front quantization, Phys. Rev. D 36 (1987) 1141.
29. A. Harindranath and J.P. Vary, Stability of the vacuum in scalar field models in 1 + 1 dimensions, Phys. Rev. D 37 (1988) 1076.
30. 4 in two-dimensions with nongaussian variational approximation, Phys. Lett. B 221 (1989) 44.
31. 4 in (1 + 1)-dimensions theory, Z. Phys. A353 (1996) 301 [hep-ph/9408355].