Gapped spin liquid states in a one-dimensional Hubbard model with antiferromagnetic exchange interaction

TL;DR

This paper investigates the phase diagram of a one-dimensional extended Hubbard model with antiferromagnetic exchange, revealing gapped and gapless spin liquid states, and how these phases depend on interaction strengths and filling.

Contribution

It provides a combined analytical and numerical analysis of the model, identifying the conditions for gapped and gapless spin liquid phases and their evolution with parameters.

Findings

Half-filling leads to a Mott insulator with a spin gap and dimerization.

Critical point U_c for phase transition depends on J, approaching zero as J increases.

Away from half-filling, the charge gap collapses while the spin gap remains.

Abstract

We study the phase diagram of a one-dimensional extended Hubbard model with antiferromagnetic exchange interaction analytically and numerically. The bosonization and transfer-matrix renormalization group methods are used in the corresponding coupling regimes. At half-filling, the system is a Mott insulator with a finite spin excitation gap if the on-site Coulomb repulsion is fairly smaller than the antiferromagnetic exchange J. This Mott-insulator is characterized by the bond-charge-density-wave order or spontaneously dimerization. In the weak-coupling regime where the spin-charge separation holds approximately, the critical point separating the gapless and gapped spin liquid phases is U_c\sim J/2. However, as J increases, the spin-charge couplings become important and the critical point U_c is significantly suppressed and eventually tends to zero as J\to \infty. Away from half-filling, the charge gap completely collapses but the spin gap persists.