# The one-dimensional Bose-Fermi-Hubbard model in the limit of fast fermions

## TL;DR

This paper derives an effective long-range interaction model for the one-dimensional Bose-Fermi-Hubbard system with fast fermions, analyzes its phase diagram analytically, and compares it with numerical DMRG results, highlighting phase separation phenomena.

## Contribution

It introduces a properly renormalized effective model with long-range interactions for the BFHM in the fast fermion limit and provides a detailed phase diagram analysis.

## Key findings

- Effective long-range RKKY-type interactions are derived.
- Phase separation between Mott insulator and charge density wave is confirmed.
- Analytic phase diagram aligns with DMRG numerical results.

## Abstract

We discuss the ground-state phase diagram of the one-dimensional Bose-Fermi-Hubbard model (BFHM) in the limit of fast fermions based on an effective boson model. We give a detailed derivation of the effective model with long-range RKKY-type interactions, discuss its range of validity and provide a deeper insight into its implications. In particular we show that integrating out the fast fermion degrees of freedom in a naive way results in an ill-behaved effective Hamiltonian and a proper renormalization is required. Based on the effective Hamiltonian, the phase diagram in the thermodynamic limit is constructed by analytic means and is compared to numerical results obtained by density matrix renormalization group (DMRG) techniques for the full BFHM. The most prominent feature of the phase diagram, the existence of a phase separation between Mott insulator (MI) and charge density wave (CDW) is discussed in depth including boundary effects.