Skip to main content
Log in

First order in the plaquette expansion

  • Original Contributions
  • Published:
Zeitschrift für Physik B Condensed Matter

Abstract

The plaquette expansion, a general non-perturbative method for calculating the properties of lattice Hamiltonian systems, is analytically investigated at the first non-trivial order for an arbitrary system. At this level the approximation describes systems with either a bounded or an unbounded spectrum, depending on simple inequalities formed from the first four cumulants. The analysis yields analytic forms for the ground state energy, mass gaps and density of states in the thermodynamic limit. An exact form for the resolvent oeprator is given for a finite number of sites, as well as the asymptotic form in the thermodynamic limit.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Hollenberg, L.C.L.: Phys. Rev. D47, 1640 (1993).

    Article  CAS  Google Scholar 

  2. Witte N.S., Hollenberg, L.C.L.: Z. Phys. B95, 531 (1994)

    Article  Google Scholar 

  3. Hollenberg, L.C.L., Witte N.S.: Phys. Rev. D50, 3382 (1994)

    Article  CAS  Google Scholar 

  4. Jones W.B., Thron W.J.: Continued Fractions-Analytic Theory and Applications. Reading Massachusetts: Addison-Wesley 1980

    Google Scholar 

  5. Lorentzen L., Waadeland H.: Continued Fractions with Applications. Amsterdam: North-Holland 1992

    Google Scholar 

  6. Seifert H.: Math. Ann.120, 75 (1947)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Witte, N.S., Hollenberg, L.C.L. First order in the plaquette expansion. Z. Phys. B - Condensed Matter 99, 101–110 (1995). https://doi.org/10.1007/s002570050016

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s002570050016

PACS

Navigation