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Residual Entropy of the Mott Insulator with No Symmetry Broken
The half-filled ground state of the Hubbard model on the hypercubic lattice
in D dimensions is studied by the Kondo-lattice theory, which is none other
than the 1/D expansion theory, but within the constrained Hilbert subspace
where no symmetry is allowed to be broken. A gap can open in the
single-particle excitation spectrum if and only if the residual entropy or
entropy at T=+0 K is nonzero. The Mott insulator with no symmetry broken, if it
is possible, is characterized by nonzero residual entropy or nonzero entropy at
T=+0 K. This conclusion is consistent with Brinkman and Rice's theory and the
dynamical mean-field theory. According to the well-known argument based on the
Bethe-ansatz solution, on the other hand, the half-filled ground state in one
dimension is the Mott insulator although its residual entropy per unit cell is
vanishing in the thermodynamic limit. Two possible explanations are given for
the contradiction between the present paper and the well-known argument.Comment: 27 page
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