Quantum Effect on the Mott Glass State in One-Dimension

Abstract

We study one-dimensional density wave, which is pinned by impurity potential and commensurate potential at half-filling. The former pinning leads to Anderson glass (AG) state while the latter pinning results in Mott insulator (MI) state. The Mott glass (MG) state, which has been found in the classical case, is located between AG state and MI state, and exhibits a gap for a single particle excitation but no gap for the collective excitation. We examine the effect of quantum fluctuation on such a MG state by calculating a soliton-formation energy and an optical conductivity at low frequencies. The self-consistent harmonic approximation is applied to calculate the spring constant for the potential, which determines the magnitude of pinning frequency. It is found that the MG state still exists for small quantum fluctuation and that further increase of the fluctuation leads to the disappearance of the MG state due to the large reduction of the soliton-formation energy. The results are discussed in terms of the local distribution of pinning frequency.