Phase Transitions in the One-Dimensional Pair-Hopping Model: a Renormalization Group Study

TL;DR

This study investigates phase transitions in a one-dimensional pair-hopping model using renormalization group and numerical methods, clarifying the existence of phase separation and spin-gap transitions under various conditions.

Contribution

It provides a two-loop renormalization group analysis combined with DMRG results to resolve controversies about phase transitions in the model.

Findings

No spin-gap transition at half-filling for positive V

Phase separation occurs away from half-filling at finite V

Spin-gap transition occurs at half-filling for negative V

Abstract

The phase diagram of a one-dimensional tight-binding model with a pair-hopping term (amplitude V) has been the subject of some controvery. Using two-loop renormalization group equations and the density matrix renormalization group with lengths L<=60, we argue that no spin-gap transition occurs at half-filling for positive V, contrary to recent claims. However, we point out that away from half-filling, a *phase-separation* transition occurs at finite V. This transition and the spin-gap transition occuring at half-filling and *negative* V are analyzed numerically.