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


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.


Hubbard Model Paramagnetic Phase Charge Order Finite Range Temperature Phase Diagram 
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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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