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DYNAMICAL RESPONSE OF QUASI ID MOTT INSULATORS.

Essler, F.H.L.Tsvelik

Published Jan 14, 2004• 0 citations
OpenAlex

Abstract

At low energies certain 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.

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At low energies certain 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.
We consider a model of one-dimensional Mott insulators coupled by a weak interchain tunneling ${t}_{\ensuremath{\perp}}.$ We first determine the single-particle Green's function of a single chain by exact field-theoretical methods and then take the tunneling into account by means of a random-phase approximation. In order to embed this approximation into a well-defined expansion with a small parameter, the Fourier transform ${T}_{\ensuremath{\perp}}(k)$ of the interchain coupling is assumed to have a small support in momentum space such that every integration over transverse wave vector yields a small factor ${\ensuremath{\kappa}}_{0}^{2}\ensuremath{\ll}1.$ When ${T}_{\ensuremath{\perp}}(0)$ exceeds a critical value, a small Fermi surface develops in the form of electron and hole pockets. We demonstrate that Luttinger's theorem holds both in the insulating and in the metallic phases. We find that the quasiparticle residue Z increases very fast through the transition and quickly reaches a value of about 0.4--0.6. The metallic state close to the transition retains many features of the one-dimensional system in the form of strong incoherent continua.
We study numerically how conservation laws affect the optical conductivity σ(ω) of a slightly doped one-dimensional Mott insulator. We investigate a regime where the average distance between charge excitations is large compared to their thermal de Broglie wavelength and a classical description is possible. Due to conservation laws, the dc conductivity is infinite and the Drude weight D is finite even at finite temperatures. Our numerical results test and confirm exact theoretical predictions for D both for integrable and non-integrable models. Small deviations from integrability induce slowly decaying modes and, consequently, low-frequency peaks in σ(ω), which can be described by a memory matrix approach.
The low-frequency dynamical response of an Anderson insulator is dominated by so-called Mott resonances: hybridization of pairs of states close in energy but separated spatially. We study the effect of interaction on Mott resonances in the model of spinful fermions (electrons) with local attraction. This model is known to exhibit a so-called pseudogap: a suppression of the low-energy, single-particle excitations. Correspondingly, the low-energy dynamical response is also reduced. However, this reduction has mostly quantitative character. In particular, the Mott formula for frequency-dependent conductivity preserves its functional asymptotic behavior at low frequencies, but with a small numerical prefactor. This result can be explained in terms of Mott resonances for electron pairs instead of single electrons.
Recent numerical results for the single-particle spectral function and optical conductivity of the two-dimensional Hubbard and t−J models are reviewed. Already for two holes in systems of sixteen to twenty sites (≥ 10% doping) a large electronic Fermi surface, compatible with Luttinger’s theorem, is observed. The full single-particle Green’s function is examined, and is shown to exhibit quasiparticle-like behavior, with dispersion consistent with the band structure of the non-interacting limit, and band width scaling approximately as J for J smaller than t. The optical conductivity of the Hubbard and t−J models is shown to have many features in common with recent experiments on copper oxide superconductors. The importance of the often neglected 3-site terms which arise in the derivation of the t−J model from the Hubbard model for optical properties is discussed.