Ground-state phase diagram of the one-dimensional Hubbard-model with an alternating potential

TL;DR

This paper maps the ground-state phase diagram of a one-dimensional Hubbard model with an alternating potential, revealing a double phase transition mechanism and the persistence of a dimerized phase under strong coupling.

Contribution

It provides the first comprehensive numerical phase diagram of this model, confirming the double transition mechanism and the existence of a dimerized phase.

Findings

Confirmed the double phase transition between Mott and band insulators.

Identified the spontaneously dimerized phase as an intermediate state.

Showed the dimerized phase persists in the strong-coupling limit.

Abstract

We investigate the ground-state phase diagram of the one-dimensional half-filled Hubbard model with an alternating potential--a model for the charge-transfer organic materials and the ferroelectric perovskites. We numerically determine the global phase diagram of this model using the level-crossing and the phenomenological renormalization-group methods based on the exact diagonalization calculations. Our results support the mechanism of the double phase transitions between Mott and a band insulators pointed out by Fabrizio, Gogolin, and Nersesyan [Phys. Rev. Lett. 83, 2014 (1999)]: We confirm the existence of the spontaneously dimerized phase as an intermediate state. Further we provide numerical evidences to check the criticalities on the phase boundaries. Especially, we perform the finite-size-scaling analysis of the excitation gap to show the two-dimensional Ising transition in the charge part. On the other hand, we confirm that the dimerized phase survives in the strong-coupling limit, which is one of the resultants of competition between the ionicity and correlation effects.