Flow Equations for the Ionic Hubbard Model

TL;DR

This paper uses continuous unitary transformations to analyze the ionic Hubbard model, revealing two phase transitions and identifying regions of band insulator, metal, and Mott insulator phases based on spin and charge gaps.

Contribution

It introduces a novel application of CUT to derive an effective Hamiltonian for the ionic Hubbard model, elucidating phase transitions and gap behaviors.

Findings

Identification of two critical points $U_{c_1}$ and $U_{c_2}$

Existence of band insulator, metal, and Mott insulator phases

Calculation of spin and charge gaps across phases

Abstract

Taking the site-diagonal terms of the one-dimensional ionic Hubbard model (IHM) as $H_0$, we employ Continuous Unitary Transformations (CUT) to obtain a "classical" effective Hamiltonian in which hopping term has been integrated out. For this Hamiltonian spin gap and charge gap are calculated at half-filling and subject to periodic boundary conditions. Our calculations indicate two transition points. In fixed $\Delta$, as $U$ increases from zero, there is a region in which both spin gap and charge gap are positive and identical; characteristic of band insulators. Upon further increasing $U$, first transition occurs at $U=U_{c_{1}}$, where spin and charge gaps both vanish and remain zero up to $U=U_{c_{2}}$. A gap-less state in charge and spin sectors characterizes a metal. For $U>U_{c_{2}}$ spin gap remains zero and charge gap becomes positive. This third region corresponds to a Mott insulator in which charge excitations are gaped, while spin excitations remain gap-less.