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Stability of RVB state with respect to charge modulations

Stability of RVB state with respect to charge modulations. Rastko Sknepnek. Iowa State University and DOE Ames Lab. In collaboration with:. Jun Liu and Joerg Schmalian. Correlation length. Very strong pairing interaction  suggests local pairing.

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Stability of RVB state with respect to charge modulations

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  1. Stability of RVB state with respect to charge modulations Rastko Sknepnek Iowa State University and DOE Ames Lab In collaboration with: Jun Liu and Joerg Schmalian

  2. Correlation length Very strong pairing interaction  suggests local pairing. Local pairing may be strongly affected by: • charge order • disorder (impurities) We assume a resonating valence bond (RVB) ground state. Is RVB state stable against charge order?

  3. Perform a toy Bogoliubov-de Gennes (mean-filed) calulation. pm = 0.2 m(1+pm) m(1-pm) Mean-field theory predicts very strong spatial variations in the gap! How important are electronic correlations?

  4. Model – t-J Hamiltonian Study the t-J Hamiltonian using variational Monte Carlo method. Minimize E{a}as function variational parameters {a}. We use J = 0.3t

  5. RVB wave function Variational parameters: (P.W. Anderson, Science,1987) m(1+pm) t m(1-pm) D+- D++ D-- Minimize with respect to: t, D+-, D++, D+-, m but fixed pm!

  6. Superconducting order parameter (Paramekanti, et al. PRB 70, 054504 (2004)) D measures local d-wave pairing. Superconductivity is characterized by the existence of Off Diagonal Long Range Order in the reduced density matrix. (Penrose&Onsager, Phys. Rev. 104, 576 (1956); Yang, Rev. Mod. Phys. 34, 694 (1962) Nieh, et al. PRB 51, 3760 (1995)) Reduced density matrix: a0is largest eigenvalue of r2 and is O(N) and Fcorresponding eigenfunction.

  7. Superconducting order parameter: Note: In a mean-field theory gap and SC order parameter are the same!

  8. We have minimized energy with respect to the 5 variational parameters. Minimization is performed on 8x8 system with 60 electrons – <n> = 0.9375. Difficulty: • local minima with very small energy differences. Requires very high precision energy evaluation.

  9. System exhibits long range superconducting order.

  10. For: Superconducting order parameter is insensitive to charge modulation!

  11. Summary • We have use variational Monte Carlo to study stability of the RVB • state to charge modulation. • This approach allows us to independently probe paring amplitude and • the superconducting order parameter. • We find that the superconducting order parameter is insensitive even relatively • large charge modulation.

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