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arXiv:cond-mat/0108382 · Physical review. B, Condensed matter

Weakly coupled one-dimensional Mott insulators

Fabian H. L. Eßler, Alexei M. Tsvelik

Published Mar 8, 2002• 110 citations
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Abstract

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.

DOI
10.1103/physrevb.65.115117

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We consider a model of one-dimensional Mott insulators coupled by a weak interchain tunneling t\ensuremath⊥.{t}_{\ensuremath{\perp}}.t\ensuremath⊥​. 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⊥(k){T}_{\ensuremath{\perp}}(k)T\ensuremath⊥​(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 \ensuremathκ02\ensuremath≪1.{\ensuremath{\kappa}}_{0}^{2}\ensuremath{\ll}1.\ensuremathκ02​\ensuremath≪1. When T\ensuremath⊥(0){T}_{\ensuremath{\perp}}(0)T\ensuremath⊥​(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 develop a theory of a hybrid state, where quasiparticles coexist with strong collective modes, taking as a starting point a model of infinitely many one-dimensional Mott insulators weakly coupled by interchain tunneling. This state exists at an intermediate temperature range and undergoes an antiferromagnetic phase transition at temperatures much smaller than the Mott-Hubbard gap. The most peculiar feature of the hybrid state is that its Fermi surface volume is unrelated to the electron density. We present a self-consistent derivation of the low-energy effective action for our model.
We use higher-dimensional bosonization to study the normal state of electrons in weakly coupled metallic chains interacting with long-range Coulomb forces. Particular attention is paid to the crossover between Luttinger and Fermi-liquid behavior as the interchain hopping ${t}_{\ensuremath{\perp}}$ is varied. Although in the physically interesting case of finite but small ${t}_{\ensuremath{\perp}}$ the quasiparticle residue does not vanish, the single-particle Green's function exhibits the signature of Luttinger-liquid behavior (i.e., anomalous scaling and spin-charge separation) in a large intermediate parameter regime. Using realistic parameters, we find that the scaling behavior in this regime is characterized by an anomalous dimension of the order of unity, as suggested by recent experiments on quasi-one-dimensional conductors. Our calculation also gives insights into the approximations inherent in higher-dimensional bosonization; in particular, we show that the replacement of a curved Fermi surface by a finite number MMM of flat patches can give rise to unphysical nesting singularities in the single-particle Green's function, which disappear only in the limit $M\ensuremath{\rightarrow}\ensuremath{\infty}$ or if curvature effects are included. We also compare our approach with other methods. This work extends our recent letter [Phys. Rev. Lett. 74, 2997 (1995)].
We investigate the Mott transition in weakly coupled one-dimensional (1D) fermionic chains. Using a generalization of dynamical mean field theory, we show that the Mott gap is suppressed at some critical hopping t{ perpendicular}{c2}. The transition from the 1D insulator to a 2D metal proceeds through an intermediate phase where the Fermi surface is broken into electron and hole pockets. The quasiparticle spectral weight is strongly anisotropic along the Fermi surface, both in the intermediate and metallic phases. We argue that such pockets would look like "arcs" in photoemission experiments.
Interchain hopping in systems of coupled chains of correlated electrons is investigated by exact diagonalization and quantum Monte Carlo methods. For two weakly coupled Hubbard chains at commensurate densities (e.g., n=1/3), the splitting at the Fermi level between bonding and antibonding bands is strongly reduced (but not suppressed) by repulsive interactions extending to a few lattice spacings. The magnitude of this reduction is directly connected to the exponent \ensuremath{\alpha} of the one-dimensional Luttinger liquid. However, we show that the incoherent part of the single-particle spectral function is much less affected by the interchain coupling. This suggests that incoherent interchain hopping could occur for intermediate \ensuremath{\alpha} values. \textcopyright{} 1996 The American Physical Society.