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Communications in Mathematical Physics

, Volume 208, Issue 3, pp 575–604 | Cite as

Low Temperature Phase Diagrams¶of Fermionic Lattice Systems

  • C. Borgs
  • R. Kotecký

Abstract:

We consider fermionic lattice systems with Hamiltonian H=H {(0)}H Q , where H {(0)} is diagonal in the occupation number basis, while H Q is a suitable “quantum perturbation”. We assume that H {(0)} is a finite range Hamiltonian with finitely many ground states and a suitable Peierls condition for excitations, while H Q is a finite range or exponentially decaying Hamiltonian that can be written as a sum of even monomials in the fermionic creation and annihilation operators. Mapping the d dimensional quantum system onto a classical contour system on a d+1 dimensional lattice, we use standard Pirogov–Sinai theory to show that the low temperature phase diagram of the quantum system is a small perturbation of the zero temperature phase diagram of the classical system, provided λ is sufficiently small. Particular attention is paid to the sign problems arising from the fermionic nature of the quantum particles.

As a simple application of our methods, we consider the Hubbard model with an additional nearest neighbor repulsion. For this model, we rigorously establish the existence of a paramagnetic phase with commensurate staggered charge order for the narrow band case at sufficiently low temperatures.

Keywords

Hubbard Model Paramagnetic Phase Charge Order Finite Range Temperature Phase Diagram 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • C. Borgs
    • 1
  • R. Kotecký
    • 2
  1. 1.Institut für Theoretische Physik, Universität Leipzig, Augustusplatz 10/11, 04109 Leipzig, Germany.¶E-mail: borgs@physik.uni-leipzig.deDE
  2. 2.Center for Theoretical Study, Charles University, Prague, Jilská 1, 110 00 Praha 1, Czech Republic¶and Theoretical Physics, Charles University, V Holešovičkách 2, 180 00 Praha 8, Czech Republic.¶E-mail: kotecky@cucc.ruk.cuni.czCZ

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