Correlation-Induced Metal Insulator Transition in a Two-Channel Fermion-Boson Model

We investigate charge transport within some background medium by means of an effective lattice model with a novel form of fermion-boson coupling. The bosons describe fluctuations of a correlated background. By analyzing ground state and spectral properties of this transport model, we show how a metal-insulator quantum phase transition can occur for the half-filled band case. We discuss the evolution of a mass-asymmetric band structure in the insulating phase and establish connections to the Mott and Peierls transition scenarios.

Figure 1

Photoemission (black) and inverse photoemission spectra (red) for the half-filled band case with ${\omega }_0=2$ at $t_f=5$ (upper panels) and $t_f=0.01$ (lower panels), where $N=12$, $N_b=15$. Dashed lines give the integrated spectral weights, e.g., $S_K^{+}(\omega -E_F)={\int }_0^{\omega }d{\omega }^{\prime }{A}_K^{+}({\omega }^{\prime }-E_F)$, where $S_K=S_K^{-}(-\infty )+S_K^{+}(\infty )=1$, and $\sum _K{S}_K=N$. Here and in what follows periodic boundary conditions were used, leading to discrete $K(N)$ wave numbers. All energies are measured in units of $t_b=1$, and $\omega$ is rescaled with respect to $E_F$.

Figure 2

Doping a perfect CDW, states with one particle removed (left panel) are connected by a six-step hopping process (see text), whereas a two-step process (right panel) relates states with an additional particle.

Figure 3

(Inverse) Photoemission for ${\omega }_0=0.5$ and $\lambda =0.01$, i.e., $t_f(\lambda ,{\omega }_0)=0.04$. Again $N=12$, but now $N_b=15$.

Figure 4

Particle-particle (${\chi }_{ee}$), respectively, particle-boson (${\chi }_{eb}$) correlation functions [upper graph], and weight of the $m$-boson state ($|c_m{|}^2$) [lower panel] in the ground state of the half-filled 1D two-channel fermion-boson model (2).