Correlation density matrix: An unbiased analysis of exact diagonalizations

Physical Review B - Condensed Matter and Materials Physics

Volumn 79, Issue 21, 2009, Pages

  Cheong, Siew Ann ^a   Henley, Christopher L ^a  

^a Laboratory of Atomic and Solid State Physics and Sibley School of Mechanical and Aerospace Engineering   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 67649970704     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.79.212402     Document Type: Article

References (26)

1. P. W. Leung and V. Elser, Phys. Rev. B 47, 5459 (1993) 10.1103/PhysRevB.47.5459
2. P. Lecheminant, B. Bernu, C. Lhuillier, L. Pierre, and P. Sindzingre, Phys. Rev. B 56, 2521 (1997), and references therein. 10.1103/PhysRevB.56.2521
3. S.-A. Cheong and C. L. Henley, Phys. Rev. B 74, 165121 (2006). 10.1103/PhysRevB.74.165121
4. S. Capponi, A. Läuchli, and M. Mambrini, Phys. Rev. B 70, 104424 (2004). 10.1103/PhysRevB.70.104424
5. We do not know any property of the CDM that distinguishes the case of purely classical correlations from that of quantum entanglement between A and B.
6. The change of viewpoint in using the fused index in Eq. 3 is a species of "partial transpose," but not at all the one introduced by A. Peres, Phys. Rev. Lett. 77, 1413 (1996). 10.1103/PhysRevLett.77.1413
7. As noted in Ref., Sec. 6.3.2, a basis state for A B in the operation-number basis may differ from the direct product |a |b by a fermion sign, since the creation operators defining it may come in a different order. A similar technicality appears in the extraction of any cluster density matrix from a wave function for the whole system: see Ref..
8. Observe that since Tr (ρ AB) =Tr (ρ A) =Tr (ρ B) =1 is true of any density matrix, we always have Tr (ρ C) 0. Then since TrA (ρ C) TrB (ρ C) =0, it follows that Tr X ν =Tr Y ν =0 for each of the SVD operators.
9. Equation 9 follows because [using Eqs. 4 5] (ρ AB, ρ A ρ B) F = ρ A ρ B = ρ A ρ B = ρ A 2 ρ B 2. We achieve the bound when ρ AB describes a pure state (norm 1), while every eigenvalue of ρ A (and necessarily of ρ B) is 1/D, i.e., when A B is in a maximally entangled state.
10. Our density matrices are averaged over degenerate ground states, if any, to restore all symmetries, as explained in Ref..
11. M.-C. Chung and I. Peschel, Phys. Rev. B 64, 064412 (2001) 10.1103/PhysRevB.64.064412
12. S.-A. Cheong and C. L. Henley, Phys. Rev. B 69, 075111 (2004). 10.1103/PhysRevB.69.075111
13. S.-A. Cheong, Ph.D. thesis, Cornell University, 2006;
14. http://hdl.handle.net/1813/11559
15. S.-A. Cheong and C. L. Henley (unpublished)
16. Ref., Chap. 7.
17. C. L. Henley and N.-G. Zhang, Phys. Rev. B 63, 233107 (2001) 10.1103/PhysRevB.63.233107
18. N.-G. Zhang and C. L. Henley, Phys. Rev. B 68, 014506 (2003). 10.1103/PhysRevB.68.014506
19. G. Spronken, R. Jullien, and M. Avignon, Phys. Rev. B 24, 5356 (1981) 10.1103/PhysRevB.24.5356
20. D. Poilblanc and E. Dagotto, Phys. Rev. B 44, 466 (1991) 10.1103/PhysRevB.44.466
21. C. Lin, F. H. Zong, and D. M. Ceperley, Phys. Rev. E 64, 016702 (2001), and references therein. 10.1103/PhysRevE.64.016702
22. Strictly speaking, a CDW operator is even under conjugation and is distinguished from staggered-flux (SF) operators that are odd. SF correlations characterize " d -density wave" states with an ordered spatial pattern of (orbital) currents, which have been realized in various spin-full ladder models. [See U. Schöllwock, S. Chakravarty, J. O. Fjaerestad, J. B. Marston, and M. Troyer, Phys. Rev. Lett. 90, 186401 (2003), and references therein.] Unfortunately, our implementation did not distinguish these cases: "CDW" in our results incorporates the "SF" operators. 10.1103/PhysRevLett.90.186401
23. This is reminiscent of the admixed terms in the quasiparticle creation operator of a Landau-Fermi liquid or perhaps of the extra terms in a scaling operator of the renormalization group.
24. M. Troyer, Ph.D. thesis, E.T.H. Zürich, 1994.
25. W. Münder, Diploma thesis, Universität München, 2008, http://www.theorie.physik.uni-muenchen.de/lsvondelft/publications/pdf/ 20080200-muender.pdf
26. S. Furukawa, G. Misguich, and M. Oshikawa, Phys. Rev. Lett. 96, 047211 (2006). 10.1103/PhysRevLett.96.047211