# Low energy quantum regimes of 1D dipolar Hubbard model with correlated hopping

## TL;DR

This paper uses bosonization to analyze the phase diagram of a one-dimensional dipolar Fermi gas, revealing the emergence of gapped phases like bond-ordered waves and Haldane phases under certain interactions.

## Contribution

It introduces a comprehensive bosonization approach to map the phase diagram, including non-perturbative effects, of a 1D dipolar Hubbard model with correlated hopping.

## Key findings

- Identification of phase boundaries in weak coupling regime.
- Discovery of gapped phases such as bond-ordered wave and Haldane phases.
- Demonstration of instability of Luttinger liquid with non-perturbative interactions.

## Abstract

We apply the bosonization technique to derive the phase diagram of a balanced unit density two-component dipolar Fermi gas in a one dimensional lattice geometry. The considered interaction processes are of the usual contact and dipolar long-range density-density type together with peculiar correlated hopping terms which can be generated dynamically. Rigorous bounds for the transition lines are obtained in the weak coupling regime. In addition to the standard bosonization description, we derive the low energy phase diagram taking place when part of the interaction is embodied non-perturbatively in the single component Hamiltonians. In this case the Luttinger liquid regime is shown to become unstable with respect to the opening of further gapped phases, among which insulating bond ordered wave and Haldane phases, the latter with degenerate edge modes.