Higher order corrections to effective low-energy theories for strongly correlated electron systems

A. L. Chernyshev, D. Galanakis, P. Phillips, A. V. Rozhkov, and A.-M. S. Tremblay
Phys. Rev. B 70, 235111 – Published 7 December 2004

Abstract

Three well-known perturbative approaches to deriving low-energy effective theories, the degenerate Brillouin-Wigner perturbation theory (projection method), the canonical transformation, and the resolvent methods, are compared. We use the Hubbard model as an example to show how, to fourth order in hopping t, all methods lead to the same effective theory, namely the tJ model with ring exchange and various correlated hoppings. We emphasize subtle technical difficulties that make such a derivation less trivial to carry out for orders higher than second. We also show that in higher orders, different approaches can lead to seemingly different forms for the low-energy Hamiltonian. All of these forms are equivalent since they are connected by an additional unitary transformation whose generator is given explicitly. The importance of transforming the operators is emphasized and the equivalence of their transformed structure within the different approaches is also demonstrated.

  • Received 9 July 2004

DOI:https://doi.org/10.1103/PhysRevB.70.235111

©2004 American Physical Society

Authors & Affiliations

A. L. Chernyshev1, D. Galanakis2, P. Phillips2, A. V. Rozhkov1, and A.-M. S. Tremblay3,4

  • 1Department of Physics, University of California, Irvine, California 92697, USA
  • 2Loomis Laboratory of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801-3080, USA
  • 3Department of Physics, Yale University, P. O. Box 208120, New Haven, Connecticut 06520-8120, USA
  • 4Département de Physique and Regroupement Québécois sur les Matériaux de Pointe, Université de Sherbrooke, Sherbrooke, Québec, Canada J1K 2R1

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Issue

Vol. 70, Iss. 23 — 15 December 2004

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