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Philosophical Magazine B

Nonlinear excitations in one-dimensional correlated insulators

Chun-Min Chang, A. H. Castro Neto, A. R. Bishop

Published Sep 1, 2001• 4 citations
Publisher

Abstract

In this work we investigate charge transport in one-dimensional insulators via semiclassical and perturbative renormalization group methods. We consider the problem of electron-electron, electron-phonon and electron-two-level system interactions. We show that nonlinear collective modes such as polarons and solitons are responsible for transport. We find a new excitation in the Mott insulator: the polaronic soliton. We discuss fhe differences between band and Mott insulators in terms of their spin spectrum and obtain the charge and spin gaps in each one of these systems. We show that electron-electron interactions provide strong renormalizations of the energy scales in the problem.

DOI
10.1080/13642810108205775

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In this work we investigate charge transport in one-dimensional insulators via semiclassical and perturbative renormalization group methods. We consider the problem of electron-electron, electron-phonon and electron-two-level system interactions. We show that nonlinear collective modes such as polarons and solitons are responsible for transport. We find a new excitation in the Mott insulator: the polaronic soliton. We discuss fhe differences between band and Mott insulators in terms of their spin spectrum and obtain the charge and spin gaps in each one of these systems. We show that electron-electron interactions provide strong renormalizations of the energy scales in the problem.
In this work we investigate charge transport in one-dimensional (1D) insulators via semi-classical and perturbative renormalization group (RG) methods. We consider the problem of electron-electron, electron-phonon and electron-two-level system interactions. We show that non-linear collective modes such as polarons and solitons are reponsible for transport. We find a new excitation in the Mott insulator: the polaronic soliton. We discuss the differences between band and Mott insulators in terms of their spin spectrum and obtain the charge and spin gaps in each one of these systems. We show that electron-electron interactions provide strong renormalizations of the energy scales in the problem.
We discuss a semiclassical calculation of low energy charge transport in one-dimensional (1D) insulators with a focus on Mott insulators, whose charge degrees of freedom are gapped due to the combination of short range interactions and a periodic lattice potential. Combining RG and instanton methods, we calculate the nonlinear AC conductivity and interpret the result in terms of multi-photon absorption. We compare the result of the semiclassical calculation for interacting systems to a perturbative, fully quantum mechanical calculation of multi-photon absorption in a 1D band insulator and find good agreement when the number of simultaneously absorbed photons is large.
As a generic model describing quasi-one-dimensional Mott and Peierls insulators, we investigate the Holstein-Hubbard model for half-filled bands using numerical techniques. Combining Lanczos diagonalization with Chebyshev moment expansion we calculate exactly the photoemission and inverse photoemission spectra, and use these to establish the phase diagram of the model. While polaronic features emerge only at strong electron-phonon couplings, pronounced phonon signatures, such as multiquanta band states, can be found in the Mott insulating regime as well. In order to corroborate the Mott to Peierls transition scenario, we determine the spin- and charge-excitation gaps by a finite-size scaling analysis based on density-matrix renormalization-group calculations.
We examine the single-particle excitation spectrum in the one-dimensional Hubbard-Holstein model at half-filling by performing a dynamical density matrix renormalization group calculation. The spin-charge separation is robust against the electron-phonon (EP) coupling, although both spinon and holon branches are affected by phonons. We find that this robustness is in sharp contrast to a rather strong influence of the EP coupling on quasiparticle properties in two dimensions. We discuss the implication of the results of recent angle-resolved photoemission spectroscopy measurements on SrCuO2\mathrm{Sr}\mathrm{Cu}{\mathrm{O}}_{2}SrCuO2​.
Effects of spin-Peierls fluctuation are examined in models of one-dimensional conductors. One-dimensional strongly correlated systems coupled to dynamical lattice distortion or polarization are examined by quantum Monte Carlo studies. Excitations are given by spinless charge solitons and neutral spin solitons when the system is doped away from a Mott insulator. A pairing mechanism due to a dynamical spin-Peierls fluctuation is discussed. Numerical results on the spin gap formation and the enhancement of pairing correlations in a dimerized t-J model and doped spin-1 Heisenberg model in one dimension are summarized.