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An extended lattice model of liquid helium four

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  • Meijer, P.H.E.
  • Scherer, W.D.

Abstract

A description of the low- and high-temperature behavior of liquid He is given in terms of an extended Matsubara-Matsuda lattice model. Paying particular attention to the kinematical interaction and to the hard core of the bosons leads to a unified theory for the low-temperature behavior and for the lambda transition. Since the hard-core boson operators in the lattice model correspond to spin one-half operators, one can interpret the hamiltonian as the hamiltonian of a magnetic system of oblate form, i.e., the x-y coupling is stronger than the z coupling. A rotation introduced in the space of these operators results in a hamiltonian consisting of three parts: one part is of the anisotropic Heisenberg form, the second contains pairs of creation-annihilation operators at different lattice sites and the third part consists of an interaction between creation-annihilation operators and the z component of the spin operators. A particular choice of the rotation angle eliminates the third part.

Suggested Citation

  • Meijer, P.H.E. & Scherer, W.D., 1975. "An extended lattice model of liquid helium four," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 80(5), pages 447-464.
    • Handle: RePEc:eee:phsmap:v:80:y:1975:i:5:p:447-464
    DOI: 10.1016/0378-4371(75)90096-5
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