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arXiv:cond-mat/9408061 · Physica B Condensed Matter

Conductivity of interacting spinless fermion systems via the high-dimensional approach

Götz Silvester Uhrig

Published Feb 1, 1995• 1 citation
arXivHTMLPDF
DOI
10.1016/0921-4526(94)00560-i

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Conductivity of interacting spinless fermion systems via the high dimensional approach

Götz Silvester Uhrig

Spinless fermions with repulsion are treated non-perturbatively by classifying the diagrams of the generating functional Φ in powers of the inverse lattice dimension 1/d. The equations derived from the first two orders are evaluated on the one- and on the two-particle level. The order parameter of the AB-charge density wave (AB-CDW) occurring at larger interaction is calculated in d = 3. The Bethe-Salpeter equation is evaluated for the conductivity σ(ω) which is found to have two peaks within the energy gap 2∆ in the AB-CDW: a remnant of the Drude peak and an excitonic resonance. Unexpectedly, σ DC does not vanish for T → 0 1 The limit of infinite dimensions d → ∞ for itinerant fermion systems [1, 2] has proven very useful for the understanding of strongly interacting electron systems [3]. The research focusses on one-particle properties in the strict limit d = ∞. There exist also some results on transport properties [4, 5]. The present contribution extends the knowledge on the AC- and DC-conductivity including 1/d-corrections in the model of spinless fermions with repulsive interaction. The results cover and the non-symmetry broken (homogeneous) phase and the AB-CDW occurring on bipartite lattices. The techniques used in the description of the latter are certainly transferable to other symmetry broken phases in related models. The Hamiltonian of the spinless fermion model at half-filling (n = 0.5) is given in second quantisation

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Microscopic Conductivity of Lattice Fermions at Equilibrium. Part II: Interacting Particles

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Spinless fermions with repulsion are treated non-perturbatively by classifying the diagrams of the generating functional Φ in powers of the inverse lattice dimension 1/d. The equations derived from the first two orders are evaluated on the one- and on the two-particle level. The order parameter of the AB-charge density wave (AB-CDW) occurring at larger interaction is calculated in d = 3. The Bethe-Salpeter equation is evaluated for the conductivity σ(ω) which is found to have two peaks within the energy gap 2∆ in the AB-CDW: a remnant of the Drude peak and an excitonic resonance. Unexpectedly, σ DC does not vanish for T → 0 1 The limit of infinite dimensions d → ∞ for itinerant fermion systems [1, 2] has proven very useful for the understanding of strongly interacting electron systems [3]. The research focusses on one-particle properties in the strict limit d = ∞. There exist also some results on transport properties [4, 5]. The present contribution extends the knowledge on the AC- and DC-conductivity including 1/d-corrections in the model of spinless fermions with repulsive interaction. The results cover and the non-symmetry broken (homogeneous) phase and the AB-CDW occurring on bipartite lattices. The techniques used in the description of the latter are certainly transferable to other symmetry broken phases in related models. The Hamiltonian of the spinless fermion model at half-filling (n = 0.5) is given in second quantisation
The Haldane hypothesis about the universality of the Luttinger liquid (LL) behavior in conducting one-dimensional fermion systems is checked numerically for the spinless fermion model with next-nearest-neighbor interactions. It is shown that for the large enough interactions the ground state can be gapless due to frustrations but at the same time might not belong to the same universality class as a simple LL. The exponents of the correlation functions for this unusual conducting state are found numerically by a finite-size method.
In a previous paper [Bischoff and Jeckelmann, Phys. Rev. B 96, 195111 (2017)] we introduced a density-matrix renormalization group method for calculating the linear conductance of one-dimensional correlated quantum systems and demonstrated it on homogeneous spinless fermion chains with impurities. Here we present extensions of this method to inhomogeneous systems, models with phonons, and the spin conductance of electronic models. The method is applied to a spinless fermion wire-lead model, the homogeneous spinless Holstein model, and the Hubbard model. Its capabilities are demonstrated by comparison with the predictions of Luttinger liquid theory combined with Bethe ansatz solutions and other numerical methods. We find a complex behavior for quantum wires coupled to interacting leads when the sign of the interaction (repulsive/attractive) differs in the wire and leads. The renormalization of the conductance given by the Luttinger parameter in purely fermionic systems is shown to remain valid in the Luttinger liquid phase of the Holstein model with phononic degrees of freedom.