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Variational two-particle density matrix calculation for the Hubbard model below half filling using spin-adapted lifting conditions

Brecht Verstichel UGent, Helen van Aggelen UGent, Ward Poelmans UGent and Dimitri Van Neck UGent (2012) PHYSICAL REVIEW LETTERS. 108(21).
abstract
The variational determination of the two-particle density matrix is an interesting, but not yet fully explored technique that allows us to obtain ground-state properties of a quantum many-body system without reference to an N-particle wave function. The one-dimensional fermionic Hubbard model has been studied before with this method, using standard two-and three-index conditions on the density matrix [J. R. Hammond et al., Phys. Rev. A 73, 062505 (2006)], while a more recent study explored so-called subsystem constraints [N. Shenvi et al., Phys. Rev. Lett. 105, 213003 (2010)]. These studies reported good results even with only standard two-index conditions, but have always been limited to the half-filled lattice. In this Letter, we establish the fact that the two-index approach fails for other fillings. In this case, a subset of three-index conditions is absolutely needed to describe the correct physics in the strong-repulsion limit. We show that applying lifting conditions [J. R. Hammond et al., Phys. Rev. A 71, 062503 (2005)] is the most economical way to achieve this, while still avoiding the computationally much heavier three-index conditions. A further extension to spin-adapted lifting conditions leads to increased accuracy in the intermediate repulsion regime. At the same time, we establish the feasibility of such studies to the more complicated phase diagram in two-dimensional Hubbard models.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
SYSTEMS
journal title
PHYSICAL REVIEW LETTERS
Phys. Rev. Lett.
volume
108
issue
21
article_number
213001
pages
5 pages
Web of Science type
Article
Web of Science id
000304250000006
JCR category
PHYSICS, MULTIDISCIPLINARY
JCR impact factor
7.943 (2012)
JCR rank
5/83 (2012)
JCR quartile
1 (2012)
ISSN
0031-9007
DOI
10.1103/PhysRevLett.108.213001
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
2911272
handle
http://hdl.handle.net/1854/LU-2911272
date created
2012-06-19 09:22:58
date last changed
2012-09-06 15:23:35
@article{2911272,
  abstract     = {The variational determination of the two-particle density matrix is an interesting, but not yet fully explored technique that allows us to obtain ground-state properties of a quantum many-body system without reference to an N-particle wave function. The one-dimensional fermionic Hubbard model has been studied before with this method, using standard two-and three-index conditions on the density matrix [J. R. Hammond et al., Phys. Rev. A 73, 062505 (2006)], while a more recent study explored so-called subsystem constraints [N. Shenvi et al., Phys. Rev. Lett. 105, 213003 (2010)]. These studies reported good results even with only standard two-index conditions, but have always been limited to the half-filled lattice. In this Letter, we establish the fact that the two-index approach fails for other fillings. In this case, a subset of three-index conditions is absolutely needed to describe the correct physics in the strong-repulsion limit. We show that applying lifting conditions [J. R. Hammond et al., Phys. Rev. A 71, 062503 (2005)] is the most economical way to achieve this, while still avoiding the computationally much heavier three-index conditions. A further extension to spin-adapted lifting conditions leads to increased accuracy in the intermediate repulsion regime. At the same time, we establish the feasibility of such studies to the more complicated phase diagram in two-dimensional Hubbard models.},
  articleno    = {213001},
  author       = {Verstichel, Brecht and van Aggelen, Helen and Poelmans, Ward and Van Neck, Dimitri},
  issn         = {0031-9007},
  journal      = {PHYSICAL REVIEW LETTERS},
  keyword      = {SYSTEMS},
  language     = {eng},
  number       = {21},
  pages        = {5},
  title        = {Variational two-particle density matrix calculation for the Hubbard model below half filling using spin-adapted lifting conditions},
  url          = {http://dx.doi.org/10.1103/PhysRevLett.108.213001},
  volume       = {108},
  year         = {2012},
}

Chicago
Verstichel, Brecht, Helen van Aggelen, Ward Poelmans, and Dimitri Van Neck. 2012. “Variational Two-particle Density Matrix Calculation for the Hubbard Model Below Half Filling Using Spin-adapted Lifting Conditions.” Physical Review Letters 108 (21).
APA
Verstichel, B., van Aggelen, H., Poelmans, W., & Van Neck, D. (2012). Variational two-particle density matrix calculation for the Hubbard model below half filling using spin-adapted lifting conditions. PHYSICAL REVIEW LETTERS, 108(21).
Vancouver
1.
Verstichel B, van Aggelen H, Poelmans W, Van Neck D. Variational two-particle density matrix calculation for the Hubbard model below half filling using spin-adapted lifting conditions. PHYSICAL REVIEW LETTERS. 2012;108(21).
MLA
Verstichel, Brecht, Helen van Aggelen, Ward Poelmans, et al. “Variational Two-particle Density Matrix Calculation for the Hubbard Model Below Half Filling Using Spin-adapted Lifting Conditions.” PHYSICAL REVIEW LETTERS 108.21 (2012): n. pag. Print.