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Journal of the Physical Society of Japan

Quantum Effect on the Mott Glass State in One-Dimension

Yoshikazu Suzumura, Masato Isobe

Published Nov 1, 2004• 1 citation
Publisher

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.

DOI
10.1143/jpsj.73.3092

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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.
We study the effect of impurity pinning on a one-dimensional half-filled electron system, which is expressed in terms of a phase Hamiltonian with the charge degree of freedom. Within the classical treatment, the pinned state is examined numerically. The Mott glass, which has been pointed out by Orignac et al. [Phys. Rev. Lett 83 (1999) 2378], appears in the intermediate region where the impurity potential competes with the commensurate potential. Such a state is verified by calculating the soliton formation energy, the local restoring force around the pinned state and the optical conductivity.
We study the low-energy limit of a quarter-filled one-dimensional Mott insulator. We analytically determine the local density of states in the presence of a strong impurity potential, which is modeled by a boundary. To this end we calculate the Green function using field theoretical methods. The Fourier transform of the local density of states shows signatures of a pinning of the spin-density wave at the impurity as well as several dispersing features at frequencies above the charge gap. These features can be interpreted as propagating spin and charge degrees of freedom. Their relative strength can be attributed to the ``quasi-fermionic'' behavior of charge excitations with equal momenta. Furthermore, we discuss the effect of bound states localized at the impurity. Finally, we give an overview of the local density of states in various one-dimensional systems and discuss implications for scanning tunneling microscopy experiments.
Competition between Mott and Anderson metal-insulator transitions is studied in a one dimensional spinless fermion system of 200 sites. Although the long range charge density wave (CDW) order and gap of the Mott phase are destroyed by weak randomness, the elementary excitations are still solitons based on the local CDW order. The solitons are easily localized in the random potential. Thus for weak randomness and large interaction, a disordered Mott phase exists in which the localization is determined by the local CDW order in contrast to the conventional Anderson localization picture in the weak interaction limit.
We determine the local density of states of one-dimensional incommensurate charge-density wave states in the presence of a strong impurity potential, which is modeled by a boundary. We find that the charge-density wave gets pinned at the impurity, which results in a singularity in the Fourier transform of the local density of states at momentum 2k_{F}. At energies above the spin gap we observe dispersing features associated with the spin and charge degrees of freedom, respectively. In the presence of an impurity magnetic field we observe the formation of a bound state localized at the impurity. All of our results carry over to the case of 1D Mott insulators by exchanging the roles of spin and charge degrees of freedom. We discuss the implications of our result for scanning tunneling microscopy experiments on spin-gap systems such as two-leg ladder cuprates.
The doped Mott insulator in one dimension has been studied based on the phase Hamiltonian with the Umklapp scattering process, in which the charge degree of freedom is described by the quantum sine-Gordon model. The well-known equivalence between the quantum sine-Gordon model and the massive Thirring model for the spinless fermion makes it clear that the Mott-Hubbard gap originates from the Umklapp scattering process as was indicated by Emery and Giamarchi. Compressibility, density-density correlation function, frequency dependence of optical conductivity and Drude weight have been calculated in the presence of the impurity scattering treated in the self-consistent Born approximation. It is seen that there exists a crossover behavior in the spectral weight of charge excitations: the acoustic mode is dominant in small wave number region while the optical excitations across the Mott-Hubbard gap lie in large wave number region and that this crossover wave number is reduced as the Mott transition is approached.
The collective excitations from the spin density wave pinned by some impurities are investigated with the self-consistent harmonic approximation applied for the phase Hamiltonian. It is found that the pinning-depinning transition due to the quantum fluctuation in the ground state cannot occur in two-dimensional nor three-dimensional isotropic system. In contrast, it has already been revealed that the quantum depinning (melting) can occur in one dimension. It suggests that the critical dimension of the quantum localization-delocalization phase transition is one, within the present approximation. The present result is also available for the charge density wave pinned by some impurities.