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arXiv:0903.5226 · Physical Review A

Fermion-mediated long-range interactions of bosons in the one-dimensional Bose-Fermi-Hubbard model

Alexander Mering, Michael Fleischhauer

Published Jan 20, 2010• 23 citations
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Abstract

The ground-state phase diagram of mixtures of spin polarized fermions and bosons in a 1D periodic lattice is discussed in the limit of large fermion hopping and half filling of the fermions. Numerical simulations performed with the density matrix renormalization group (DMRG) show in addition to bosonic Mott insulating (MI), superfluid (SF), and charge density-wave phases (CDW) a yet unreported phase with spatial separation of MI and CDW regions. We derive an effective bosonic theory which allows for a complete understanding and quantitative prediction of the bosonic phase diagram. In particular the origin of CDW phase and the MI-CDW phase separation is revealed as an effective fermion-mediated long-range interaction between bosons with alternating sign.

DOI
10.1103/physreva.81.011603

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The authors 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. The authors give a detailed derivation of the effective model with long‐range Rudermann–Kittel–Kasuya–Yosida (RKKY)‐type interactions, discuss its range of validity, and provide a deeper insight into its implications. In particular, they 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.
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