Communications in Mathematical Physics

, Volume 206, Issue 2, pp 289–335 | Cite as

Effective Interactions Due to Quantum Fluctuations

  • Roman Kotecký
  • Daniel Ueltschi


A class of quantum lattice models is considered, with Hamiltonians consisting of a classical (diagonal) part and a small off-diagonal part (e.g. hopping terms). In some cases when the classical part has an infinite degeneracy of ground states, the quantum perturbation may stabilize some of them. The mechanism of this stabilization stems from effective potential created by the quantum perturbation.

Conditions are found when this strategy can be rigorously controlled and the low temperature phase diagram of the full quantum model can be proven to be a small deformation of the zero temperature phase diagram of the classical part with the effective potential added. As illustrations we discuss the asymmetric Hubbard model and the Bose–Hubbard model.


Effective Potential Hubbard Model Small Deformation Effective Interaction Zero Temperature 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Roman Kotecký
    • 1
  • Daniel Ueltschi
    • 2
  1. 1.Center for Theoretical Study, Charles University, Jilská 1, 110 00 Praha 1, Czech RepublicCZ
  2. 2. Department of Theoretical Physics, Charles University, V Holešovičkách 2, 180 00 Praha 8, Czech Republic. E-mail: kotecky@cucc.ruk.cuni.czDE

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