From Gapped Excitons to Gapless Triplons in One Dimension

TL;DR

This paper investigates the elementary excitations in the ionic Hubbard model in one dimension, revealing the transition from gapped excitons to gapless triplons across different phases using continuous unitary transformations.

Contribution

It introduces a controlled CUT approach starting from a dimerized system to accurately determine charge and spin excitation dispersions in the model.

Findings

Identifies the evolution from gapped excitons to gapless triplons.

Provides dispersion relations for charge and spin excitations.

Analyzes bound states across phase transitions.

Abstract

Often, exotic phases appear in the phase diagrams between conventional phases. Their elementary excitations are of particular interest. Here, we consider the example of the ionic Hubbard model in one dimension. This model is a band insulator (BI) for weak interaction and a Mott insulator (MI) for strong interaction. Inbetween, a spontaneously dimerized insulator (SDI) occurs which is governed by energetically low-lying charge and spin degrees of freedom. Applying a systematically controlled version of the continuous unitary transformations (CUTs) we are able to determine the dispersions of the elementary charge and spin excitations and of their most relevant bound states on equal footing. The key idea is to start from an externally dimerized system using the relative weak interdimer coupling as small expansion parameter which finally is set to unity to recover the original model.