Abstract
We consider Fermion systems on integer lattices. We establish the existence of dynamics for a class of long range interactions. The infinite volume ground states are considered. The equivalence of the variational principle and ground state conditions is proved for long range interactions. We also prove that any pure translationally invariant ground state of the gauge invariant algebra is extendible to a ground state of the full CAR algebra for the Hamiltonian with a chemical potential (equivalence of ensemble for canonical and ground canonical states at the zero temperature).
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Araki, H., Kishimoto, A.: Symmetry and equilibrium states. Commun. Math. Phys.53, 211–232 (1977)
Araki, H., Haag, R., Kastler, D., Takesaki, M.: Extension of KMS States and Chemical Potential. Commun. Math. Phys.53, 97–134 (1977)
Bratteli, O., Jørgensen, P. (eds.): Positive semigroups of operators, and applications. Acta Appl. Math.2, Nos. 3/4 (1984)
Bratteli, O., Kishimoto, A., Robinson, D.: Ground states of quantum spin systems. Commun. Math. Phys.64, 41–48 (1978)
Bratteli, O., Robinson, D.: Operator algebras and quantum statistical mechanics I, II. Berlin-Heidelberg-New York: Springer, 1979
Davies, E.B.: Quantum Theory of Open Systems. London-New York: Academic Press, 1976
Davies, E.B., Lindsay, M.: Superderivations and Symmetric Markov Semigroups. Commun. Math. Phys.157, 359–370 (1993)
Georgii, H. Canonical Gibbs Measures. Springer Lect. Note in Math.760, Berlin-Heidelberg-New York: Springer
Georgii, H.: Gibbs Measures and Phase Transitions. Amsterdam: Walter de Gruyter, 1988
Gottstein, C.T., Werner, R.: Ground states of infiniteq-deformed Heisenberg ferromagnet. Preprint, Osnabrück, 1994
Liggett, T.M.: Interacting Particle Systems. Berlin-Heidelberg-New York: Springer, 1981
Lindblad, G.: On the Generator of Quantum Dynamical Semigroups. Commun. Math. Phys.48, 119–130 (1976)
Matsui, T.: Markov semigroups on UHF algebras. Rev. Math. Phys.5, 587–600 (1993)
Matsui, T.: Quantum Statistical Mechanics and Feller Semigroup, Preprint
Paulsen, V.I.: Completely Bounded Maps and Dilations. Pitman Research Notes in Mathematics Series146, London: Longman
Richter, S., Werner, R.: Ergodicity of Quantum Cellular Automata. J. Stat. Phys.82, 963–998 (1996)
Ruelle, D.: Thermodynamic Formalism. Reading, MA: Addisson Wesley, 1978
Simon, B.: Statistical Mechanics of Lattice Gases I. Princeton, NJ: Princeton Univ. Press, 1993
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Communicated by H. Araki
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Matsui, T. Ground states of Fermions on lattices. Commun.Math. Phys. 182, 723–751 (1996). https://doi.org/10.1007/BF02506423
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DOI: https://doi.org/10.1007/BF02506423