Weakly coupled one-dimensional Mott insulators

Abstract

We consider a model of one-dimensional Mott insulators coupled by a weak interchain tunnelling t ⊥ . We first determine the single-particle Green's function of a single chain by exact field-theoretical methods and then take the tunnelling into account by means of a Random Phase Approximation (RPA). In order to embed this approximation into a well-defined expansion with a small parameter, the Fourier transform T ⊥ (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 κ 2 0 ≪ 1. When T ⊥ (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 quasi-particle 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.

Effective theory of Fermi pockets in fluctuating antiferromagnets

“…(3.10). They explain the violation of the Luttinger theorem by zeros of the Green's function 54,55,58 ; the connection of these zeros to our work was discussed below Eq. (3.10).…”

Theory of the Luttinger surface in doped Mott insulators

“…In systems lacking quasiparticles ͑no poles͒, such as insulators, the Landau correspondence between the particle density and quasiparticle excitations breaks down. In fact, as uncloaked recently, 3,6,7 Luttinger's theorem is not necessarily invalidated when quasiparticles are absent. The suggestion [6][7][8] is that the particle density…”

Breakup of the Fermi Surface Near the Mott Transition in Low-Dimensional Systems

“…According to Luttinger's theorem, the area of the Brillouin zone where ReGk; 0 > 0 equals the electron density and is thus conserved [12,24]. In the Mott phase ReGk; 0 changes sign at k =2 due to the divergence of k; 0 [ Fig.…”

“…Such systems exhibit a deconfinement transition between a one-dimensional Mott insulator and a three-dimensional metal. For such systems, FS pockets were found when the interchain coupling is treated within the RPA approximation [12]. The pockets form when the interchain bandwidth exceeds the 1D Mott gap of the chains.…”