Dynamical Response of Quasi 1D Mott Insulators

Abstract

Abstract. At low energies cert.ain one dimensional Mott insulators can be described in terms of an exactly solvable quantum field theory, the U(1) Thirring model. Using exact results derived from integrability we determine dynamical properties like the frequency dependent optical conductivity and the single-particle Green's function. We discuss the effects of a small temperature and the effects on interchain tunneling in a model of infinitely many weakly coupled chains. I IntroductionThe problem of the Mott metal-insulator transition, which is a paradigm for the importance of electron-electron interactions, has been the subject of great interest [l] since the pioneering works by Mott [2]. The intrinsic difficulty in describing the Mott transition quantitatively is that it occurs when the kinetic and potential energies are of the same order. This regime is difficult to access from either the "band" (where one diagonalizes the kinetic energy first and then takes electronelectron interactions into account perturbatively) or the "atomic" (where one diagonalizes the electron-electron interaction first and then takes the hopping into account perturbatively) limits. In recent years much progress in understanding the Mott transition has been made based on the so-called Dynamical Mean Field theory, which considers a lattice in infinitely many dimensions D --i 00 (see Ref.[3] and references therein). Here we are concerned with the rather different situation, where the tunneling along one lattice direction is much larger than along all others. The resulting system can be thought of in terms of weakly coupled chains of electrons and will be referred to as a quasi one dimensional Mott insulator. When the band is half-filled and the interchain tunneling is switched off, Umklapp processes dynamically generate a spectral gap M and we are dealing with an ensemble of uncoupled 1D Mott insulating chains. The same Umklapp scattering mechanism can generate gaps at any commensurate flling e.g. quarter filling, but only if the interactions are sufficiently strong. There are two questions we want to address: (i) What is the dynamical response of the uncoupled Mott-insulating chains system? and (ii) What are the effects of a weak interchain tunneling? Examples of materials that are believed to fall into the general category of quasi-1D Mott insulators are the Bechgaard salts {4] and chain cuprates like SrCuO2, Sr2CuO3 ' or PrBazCu307. They have been found to exhibit very rich and unusual physical properties such as spin-charge separation [5, 61.IMore precisely, these compounds are considered to be chargetransfer insulators. The ModelsThe simplest models used in the description of one dimensional Mott insulators are "extended" Hubbard models of the formwhere n k , , = cL,,ck,, and n k = n k ,~ + n k . 1 are electron number operators. The electron-electron interaction terms mimic the effects of a screened Coulomb interaction. Two cases are of particular interest from the point of view of application to e.g. the Bechgaard salts [4, 71: ...

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