Lattice Green Functions on a Two-Dimensional Rectangular Lattice with Next-Nearest Neighbor Interaction

• Authors: M. Bak
• Languages of publication: EN

Abstracts

EN

The analytic formula for the on-site Green function on the two-dimensional rectangular lattice is shown for arbitrary energy, both within the band (complex Green function) and outside the band (real Green function), expressed by means of elliptic integrals. The recursion formulae enabling calculation of the Green functions on other lattice sites are shown.

Keywords

EN

02.30.Gp; 02.30.Uu; 02.60.Nm; 71.15.-m; 02.70.Hm; 71.10.Fd

Discipline

• 02.70.Hm: Spectral methods
• 71.10.Fd: Lattice fermion models (Hubbard model, etc.)
• 02.30.Uu: Integral transforms
• 71.15.-m: Methods of electronic structure calculations(see also 31.15.-p Calculations and mathematical techniques in atomic and molecular physics; for electronic structure calculations of superconducting materials, see 74.20.Pq)
• 02.30.Gp: Special functions
• 02.60.Nm: Integral and integrodifferential equations

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2010
• Volume: 118
• Issue: 2
• Pages: 386-388

Dates

published

2010-08

Contributors

author

M. Bak

• Faculty of Physics, A. Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland

References

• 1. R.G. Boyd, J. Callaway, Phys. Rev. 140, A1621 (1965)
• 2. S. Krompiewski, Acta Phys. Pol. A 53, 845 (1978)
• 3. A.A. Bahurmuz, Acta Phys. Pol. A 57, 565 (1980)
• 4. T. Morita, J. Phys. A, Math. Gen. 8, 478 (1975)
• 5. D.Y. Xing, M. Liu, C.D. Gong, Phys. Rev. B 44, 12525 (1991)
• 6. T. Horiguchi, T. Morita, J. Phys. C, Solid State Phys. 8, L232 (1975)

Identifiers

DOI

10.12693/APhysPolA.118.386