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Normal He3: an almost localized Fermi liquid

Dieter Vollhardt

Dieter Vollhardt

  • Max-Planck-Institut für Physik und Astrophysik, Werner Heisenberg-Institut für Physik, D-8000 München 40, Federal Republic of Germany

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Rev. Mod. Phys. 56, 99 – Published 1 January, 1984

DOI: https://doi.org/10.1103/RevModPhys.56.99

Abstract

The Hubbard model is used to calculate static properties of normal-liquid He3 at T=0. For this, Gutzwiller's variational approach to that model is employed. The work is based on an observation by Anderson and Brinkman that the results of this method, obtained by Brinkman and Rice for the metal-insulator transition in the case of one particle per site, appear to be in qualitative agreement with the experimentally measured properties of that liquid. In this sense normal He3 can be understood to be close to a localization transition of the particles where their effective mass diverges. The incipient localization is found to determine the properties of that liquid. Hence He3 is "almost localized" rather than "almost ferromagnetic," as often claimed by paramagnon theory. The author further investigates this motion. Discussing Gutzwiller's approach to the Hubbard model, he shows that it is well suited for a description of a liquid system like He3. The approach and its physical implications are investigated by means of the reformulation of the solution due to Ogawa et al. It is shown explicitly that Gutzwiller's results can be placed into the concepts of Landau-Fermi-liquid theory and that within this model the Landau parameters F0s and F0a are related. Furthermore, the author identifies two different kinds of spin-fluctuation processes inherent to the model, one of which is shown to be responsible for the largeness of F0s. Going beyond these qualitative aspects, the author evaluates F0a and F0s quantitatively, finding that F0a agrees very well with the experimentally determined values at all pressures, with F0a→−34p at high pressures, where p is always close to unity. Hence the system is never close to a ferromagnetic transition. By means of the forward scattering sum rule for l<2 an analytic expression for F1a is obtained. Finally, the author extends the analysis to large magnetic fields, finding that in the case of normal He3 the magnetization increases very rapidly with the magnetic field. This is due to the large zero-field effective mass. There is a line of critical values for the interaction and the magnetic field where a fully magnetized state is formed via a first-order transition. Calculating the drop in melting pressure due to the magnetic field, the author finds that it essentially removes the minimum in the melting curve. Thus the melting pressure even of fully polarized He3 is larger than zero, in agreement with arguments by Castaing and Nozières.

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Rev. Mod. Phys. 56, 99– Published 1 January, 1984

    © 1984 American Physical Society

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