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International Journal of Modern Physics B

Spin-Charge coupling in doped Mott Insulators

J. M. Wheatley, A. J. Schofield

Published Mar 1, 1992• 19 citations
Publisher

Abstract

The coupling of charge to spin degrees of freedom in two dimensional doped Mott insulators is briefly reviewed. The problem of the long-wavelength charge response is mapped to the response of a Bose system coupled to a fictitious electromagnetic field. We describe an approach to the conductivity and diamagnetic response in this model.
DOI
10.1142/s0217979292000396

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We study spin and charge dynamics of stripes in doped Mott insulators by considering a two-dimensional Hubbard model with N fermion flavors. For N = 2 we recover the normal one-band model while for N → ∞ a spin density wave mean-field solution. For all band fillings, lattice topologies and N = 4 n , the model may be solved by means of quantum Monte Carlo methods without encountering the sign problem. At N = 4 and in the vicinity of the Mott insulator we find a stripe phase. This phase has a quasiparticle gap but conducts due to long-wavelength low-lying collective charge modes.
Junctions of doped Mott insulators offer a route to rectification at frequencies beyond the terahertz range. Mott insulators have strong electronic correlations and therefore short timescales for electron-electron scattering. It is this short time scale that allows for the possibility of rectification at frequencies well beyond those of semiconductor devices that are limited by the slow diffusion of charge carriers. We model a junction by a one dimensional chain of electrons with p- and n-doping on the two halves of the chain. Two types of systems are investigated: spin polarized electrons with nearest-neighbor interaction, and spin-half electrons that interact via on-site repulsion (the Hubbard model). For short chains the many-body Schrodinger equation can be integrated numerically exactly, and when driven by an oscillating electromagnetic field such idealized junctions rectify, showing a preferred direction for charge transfer. Longer chains are studied by the time-dependent density-matrix renormalization-group method, and also shown to rectify.
Abstract—Junctions of doped Mott insulators offer a route to rectification at frequencies beyond the terahertz range. Mott insulators have strong electronic correlations and therefore short timescales for electron-electron scattering. It is this short time scale that allows for the possibility of rectification at frequencies higher than those of semiconductor devices that are limited by the slow diffusion of charge carriers. We model a junc-tion by a one dimensional chain of electrons with p- and n-doping on the two halves of the chain. Two types of systems are investigated: spin polarized electrons with nearest-neighbor interaction, and spin-half electrons that interact via on-site repulsion (the Hubbard model). For short chains the many-body Schrödinger equation can be integrated numerically exactly, and when driven by an oscillating electromagnetic field such idealized junctions rectify, showing a preferred direction for charge transfer. Longer chains are studied by the time-dependent density-matrix renormalization-group method, and also shown to rectify. I.
Recent angle-resolved photoemission spectroscopy (ARPES) for a newly discovered doped one-dimensional (1D) Mott insulator ${\mathrm{Ba}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{3+\ensuremath{\delta}}$ proposed the presence of attractive charge interactions between neighboring sites if a 1D Hubbard model is employed to describe the material. On the other hand, long-range repulsive charge interactions were proposed to be crucial for understanding the optical excitations of undoped 1D Mott insulators. Motivated by these contrasting proposals, we perform density-matrix renormalization group calculations of the single-particle spectral function as well as dynamical spin and charge structure factors for two kinds of extended 1D Hubbard models. The spectral function for the long-range repulsive model less agrees with the ARPES data as compared with that for the attractive one. The dynamical spin and charge structure factors also exhibit contrasting behaviors between the two models: The attractive model shows less momentum dependence of the integrated weight in the dynamical spin structure factor and more accumulation of the weight on the upper edge of particle-hole-type excitation in the dynamical charge structure factor. These features give a good criterion of an appropriate model for doped 1D Mott insulators, which can be judged by resonant-inelastic x-ray scattering experiments.
The one-dimensional Hubbard model is characterized by charge-spin separation, but nevertheless in the doped system \ensuremath{\sigma}(\ensuremath{\omega}>0) does not vanish due to a small remaining coupling between charge and spin degrees of freedom. We derive an effective Hamiltonian and give in leading order (\ensuremath{\sim}J2{\mathit{J}}^{2}J2) an analytic expression for \ensuremath{\sigma}(\ensuremath{\omega}) for the case of the Mott insulator doped with one hole. The complete frequency dependence in the strong-coupling limit of the Hubbard model and for the t-J model agrees with results from exact diagonalization. The limit \ensuremath{\sigma}(\ensuremath{\omega}\ensuremath{\rightarrow}0) at T=0 is found to be very different for the two models, i.e., \ensuremath{\sim}${\mathrm{\ensuremath{\omega}}}^{3/2}$ in the strong-coupling limit and \ensuremath{\sim}${\mathrm{\ensuremath{\omega}}}^{\mathrm{\ensuremath{-}}1/2}$ for the t-J model.
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.