Advertisement

Communications in Mathematical Physics

, Volume 64, Issue 1, pp 41–48 | Cite as

Ground states of quantum spin systems

  • Ola Bratteli
  • Akitaka Kishimoto
  • Derek W. Robinson
Article

Abstract

We prove that ground states of quantum spin systems are characterized by a principle of minimum local energy and that translationally invariant ground states are characterized by the principle of minimum energy per unit volume.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Minimum Energy 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bratteli, O., Robinson, D.W.: Operator algebras and quantum statistical mechanics. Berlin, Heidelberg, New York: Springer (to appear)Google Scholar
  2. 2.
    Sewell, G.L.:KMS conditions and local thermodynamic stability. II. Commun. math. Phys.55, 53 (1977)Google Scholar
  3. 3.
    Araki, H.: OnKMS states of aC*-dynamical system, inC*-algebras and applications to physics. Lecture notes in mathematics, Vol. 650. Berlin, Heidelberg, New York: Springer 1978Google Scholar
  4. 4.
    Bratteli, O., Kishimoto, A., Robinson, D.W.: Stability properties and theKMS condition. Commun. math. Phys.61, 209 (1978)Google Scholar
  5. 5.
    Araki, H., Sewell, G.L.:KMS conditions and local thermodynamic stability of quantum lattice systems. Commun. math. Phys.52, 103 (1977)Google Scholar
  6. 6.
    Ruelle, D.: Statistical mechanics. New York-Amsterdam: Benjamin 1969Google Scholar
  7. 7.
    Lanford, O.E., Robinson, D.W.: Statistical mechanics of quantum spin systems. III. Commun. math. Phys.9, 327 (1968)Google Scholar
  8. 8.
    Araki, H.: On the equivalence of theKMS condition and the variational principle for quantum lattice systems. Commun. math. Phys.38, 1 (1974)Google Scholar
  9. 9.
    Ruelle, D.: Some remarks on the ground state of infinite systems in statistical mechanics. Commun. math. Phys.11, 339 (1968)Google Scholar
  10. 10.
    Bratteli, O.: Conservation of estimates in quantum field theory. Commun. Pure Appl. Math.25, 759 (1972)Google Scholar
  11. 11.
    Powers, R.: Representations of uniformly hyperfinite algebras and their associated von Neumann rings. Ann. Math.86, 138 (1967)Google Scholar
  12. 12.
    Borchers, H.: Energy and momentum as observables in quantum field theory. Commun. math. Phys.2, 49 (1966)Google Scholar
  13. 13.
    Arveson, W.: On groups of automorphisms of operator algebras. J. Funct. Anal.15, 217 (1974)Google Scholar
  14. 14.
    Bratteli, O., Kishimoto, A.: Generation of semi-groups, and two-dimensional quantum lattice systems. J. Funct. Anal. (to appear)Google Scholar
  15. 15.
    Elliott, G.: Derivations of matroidC*-algebras. Inventiones Math.9, 253 (1970)Google Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • Ola Bratteli
    • 1
  • Akitaka Kishimoto
    • 1
  • Derek W. Robinson
    • 1
    • 2
  1. 1.Centre de Physique Théorique II, CNRSMarseille Cedex 2France
  2. 2.Department of MathematicsUniversity of N.S.W.SydneyAustralia

Personalised recommendations