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The half-filled ground state of the Hubbard model on the hypercubic latticein D dimensions is studied by the Kondo-lattice theory, which is none otherthan the 1/D expansion theory, but within the constrained Hilbert subspacewhere no symmetry is allowed to be broken. A gap can open in thesingle-particle excitation spectrum if and only if the residual entropy orentropy at T=+0 K is nonzero. The Mott insulator with no symmetry broken, if itis possible, is characterized by nonzero residual entropy or nonzero entropy atT=+0 K. This conclusion is consistent with Brinkman and Rice's theory and thedynamical mean-field theory. According to the well-known argument based on theBethe-ansatz solution, on the other hand, the half-filled ground state in onedimension is the Mott insulator although its residual entropy per unit cell isvanishing in the thermodynamic limit. Two possible explanations are given forthe contradiction between the present paper and the well-known argument.

Residual Entropy of the Mott Insulator with No Symmetry Broken