Charge and Spin Gap Formation in Exactly Solvable Hubbard Chains with Long-Rang Hopping

TL;DR

This paper investigates charge and spin gap formation in exactly solvable Hubbard chains with long-range 1/r hopping, revealing unique transition behaviors and transport properties near the Mott-Hubbard transition.

Contribution

It introduces exactly solvable models with long-range hopping to analyze charge and spin insulator transitions using conformal field theory and g-ology techniques.

Findings

Charge insulator transition involves an infinite discontinuity in Drude weight.

Magnetic properties align with strongly correlated electron systems.

Charge transport near the Mott-Hubbard transition shows non-generic behavior.

Abstract

We discuss the transition from a metal to charge or spin insulating phases characterized by the opening of a gap in the charge or spin excitation spectra, respectively. These transitions are addressed within the context of two exactly solvable Hubbard and tJ chains with long range, $1/r$ hopping. We discuss the specific heat, compressibility, and magnetic susceptibility of these models as a function of temperature, band filling, and interaction strength. We then use conformal field theory techniques to extract ground state correlation functions. Finally, by employing the $g$-ology analysis we show that the charge insulator transition is accompanied by an infinite discontinuity in the Drude weight of the electrical conductivity. While the magnetic properties of these models reflect the genuine features of strongly correlated electron systems, the charge transport properties, especially near the Mott-Hubbard transition, display a non-generic behavior.