Charge Excitations in Doped Mott Insulator in One Dimension

TL;DR

This paper investigates charge excitations in a doped one-dimensional Mott insulator using the sine-Gordon model, revealing a crossover in spectral weight from acoustic to optical modes near the Mott transition.

Contribution

It provides a detailed analysis of charge excitations and their spectral crossover in a doped 1D Mott insulator, connecting the sine-Gordon and Thirring models.

Findings

Crossover in spectral weight from acoustic to optical excitations.

Optical excitation gap decreases approaching the Mott transition.

Charge excitation behavior depends on wave number and doping level.

Abstract

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.