Almost all Mott insulators ever existing have been known to have the translational-symmetry broken ground states such as antiferromagnetism and dimerization. It has been a remaining fundamental issue whether the genuine Mott insulator without any translational symmetry breaking is realized except in one spatial-dimension systems, since P. W. Anderson's proposal in 70's.
To resolve this problem, we applied the newly-developed numerical algorithm "the path integral renormalization group method"to the half-filled Hubbard model on the geometrically frustrated lattices in the two dimension [1,2]. The nonmagnetic-insulator phase sandwiched by the the paramagnetic-metal phase and the antiferromagnetic-insulator phase shows evidence against translational symmetry breaking of the dimerized state, plaquette singlet state, staggered flux state, and charge ordered state.
These results support that the genuine Mott insulator which cannot be adiabatically continued to the band insulator is realized generically by Umklapp scattering through the effects of geometrical frustration and
quantum fluctuation in the two-dimensional system [1,2].
[1] H. Morita, S. Watanabe and M. Imada: J. Phys. Soc. Jpn. 71 (2002) 2109.
[2] S. Watanabe: J. Phys. Soc. Jpn. 72 (2003) 2042.
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Last updated: May 15 2016