The ground state of the plane quantum Fermi crystal with a triangular lattice is considered. Using symmetry properties, the ground state wave function is constructed and a variational estimate of the ground state energy is obtained. The ground state corresponds to an unsaturated ferromagnet with spin equal to one-third of the maximum spin. Some other nonalternate lattices are also considered. The spectrum of elementary excitations for a finite concentration of the vacancies is studied. The existence of low-lying spin excitations with a small gap is predicted. Ordinary gapless spin waves also exist.
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Iordansky, S.V. Magnetic properties of vacancies on the triangular plane 3He crystal. J Low Temp Phys 40, 401–413 (1980). https://doi.org/10.1007/BF00117125
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DOI: https://doi.org/10.1007/BF00117125