Dynamical correlation functions of one-dimensional superconductors and Peierls and Mott insulators

Abstract

I construct the spectral function of the Luther-Emery model which describes one-dimensional fermions with one gapless and one gapped degree of freedom, i.e. superconductors and Peierls and Mott insulators, by using symmetries, relations to other models, and known limits. Depending on the relative magnitudes of the charge and spin velocities, and on whether a charge or a spin gap is present, I find spectral functions differing in the number of singularities and presence or absence of anomalous dimensions of fermion operators. I find, for a Peierls system, one singularity with anomalous dimension and one finite maximum; for a superconductor two singularities with anomalous dimensions; and for a Mott insulator one or two singularities without anomalous dimension. In addition, there are strong shadow bands. I generalize the construction to arbitrary dynamical multi-particle correlation functions. The main aspects of this work are in agreement with numerical and Bethe Ansatz calculations by others. I also discuss the application to photoemission experiments on 1D Mott insulators and on the normal state of 1D Peierls systems, and propose the Luther-Emery model as the generic description of 1D charge density wave systems with important electronic correlations.

Spectral functions for the tomonaga-luttinger and luther-emery liquids

“…Several authors have made progress in this direction, see Refs. 21,22, and in section III we extend and correct their study and obtain exact expressions for the single hole spectral function at the free fermion point for temperatures much smaller than the spin gap. Some technical details are relegated to appendices.…”

A brief introduction to Luttinger liquids

“…However even here, charge-spin separation still is seen, e.g. in photoemission both in theory [20] and in experiments on SrCuO 2 [22]. Moreover, far above the (charge or spin) gaps, they should no longer influence the physics, and genuine Luttinger liquid behavior is expected there.…”

“…Alternatively, the electron-phonon interaction could lead to the opening of a spin gap, and thereby destabilize the Luttinger liquid. This situation is described by a different model due to Luther and Emery, but the correlation functions continue to carry certain remnants of Luttinger physics, like non-universal power laws stemming from the gapless charges (the system remains conducting), and charge-spin separation [20].…”

Peierls to superfluid crossover in the one-dimensional, quarter-filled Holstein model

“…The latter has been studied intensely in Holstein-type models with and without spin, see discussion in section 2. The metallic Peierls state may be regarded as a more general concept for quasi-one-dimensional systems, applicable to noncommensurate fillings or the normal state (T > T c ) of a Peierls insulator [6]. On the level of bosonization, a metallic state with dominant 2k F charge correlations requires a finite spin gap [6].…”

“…The metallic Peierls state may be regarded as a more general concept for quasi-one-dimensional systems, applicable to noncommensurate fillings or the normal state (T > T c ) of a Peierls insulator [6]. On the level of bosonization, a metallic state with dominant 2k F charge correlations requires a finite spin gap [6]. In the anti-adiabatic limit, the lattice adjusts instantaneously to the electronic motion, and the Holstein model maps onto the attractive Hubbard model with dominant pairing correlations.…”