The one-dimensional Bose-Fermi-Hubbard model in the heavy-fermion limit

TL;DR

This paper investigates the phase diagram of a one-dimensional Bose-Fermi-Hubbard model at zero temperature, combining analytical strong-coupling expansion and numerical DMRG methods to identify phase boundaries and correlation behaviors.

Contribution

It provides a combined analytical and numerical analysis of the phase diagram for the Bose-Fermi-Hubbard model in the heavy-fermion limit, revealing glass-like correlations.

Findings

Analytical phase boundaries between different phases.

Exponential decay of correlations in partially compressible phases.

Comparison of perturbation theory results with DMRG data.

Abstract

We study the phase diagram of the zero-temperature, one-dimensional Bose-Fermi-Hubbard model for fixed fermion density in the limit of small fermionic hopping. This model can be regarded as an instance of a disordered Bose-Hubbard model with dichotomic values of the stochastic variables. Phase boundaries between compressible, incompressible (Mott-insulating) and partially compressible phases are derived analytically within a generalized strong-coupling expansion and numerically using density matrix renormalization group (DMRG) methods. We show that first-order correlations in the partially compressible phases decay exponentially, indicating a glass-type behaviour. Fluctuations within the respective incompressible phases are determined using perturbation theory and are compared to DMRG results.