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Physical Review B

Metal-insulator phase transition in an exactly solvable model of nondegenerate interacting fermion chains

Igor N. Karnaukhov

Published Jun 4, 2010• 0 citations
Publisher

Abstract

A two parametric family of the models of two coupled nondegenerate fermion chains is proposed and solved by the means of the Bethe ansatz. We give a detailed analysis of the exact zero-temperature phase diagram at half filling for different parameters of the interactions. It is shown that insulator and ``interchain ferromagnetic'' phase states are separated by ``intermediate metallic'' state, these phase states coexist in a tricritical point. The critical fluctuations are described by a conformal field theory with the central charge $c=1$. In the tricritical point the fermion state is described as a Luttinger liquid state with one gapless mode that is characterized by abnormal large density-density correlations and correlations of the momentum distribution function.

DOI
10.1103/physrevb.81.245106

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We propose a strongly correlated (1+1)D electron model with particle–hole asymmetry which is exactly solvable by means of the nested Bethe ansatz. The particle–hole asymmetry in this many-body system causes a metal–insulator transition with a phase separation. Here, we give a detailed analysis of the zero-temperature phase diagram of the model and demonstrate how this unusual behavior of the metal–insulator transition with phase separation arises. In particular, we show that a homogeneous phase of itinerant electrons and a mixed phase of itinerant electrons and localized electron pairs (for which two different species reside in spatially separated regions) define the ground state of a fermion chain. We also find that the metal–insulator phase transition induces phase transition on the surface with simultaneous generation of the interphase boundary.
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We study the interplay between an on-site Hubbard repulsion and quasiperiodic potential in one-dimensional fermion chains using the density matrix renormalization group. We find that, at half filling, the quasiperiodic potential can destroy the Mott gap, leading to a metallic Luttinger liquid phase between the gapped Mott insulator at strong repulsion and the localized gapless Aubry-Andr\'e insulator at strong quasiperiodic potential. Away from half filling, the metallic phase of the interacting model persists to larger critical strengths of the potential than in the noninteracting case, suggesting interaction-stabilized delocalization at finite doping. We characterize the Luttinger liquid through its charge and spin correlations, structure factors, and entanglement entropy.