arXiv subjects

Alexander Mering

Publications and source records attributed to Alexander Mering.

5 recordsLinked to original sources

arXiv2019

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

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.

cond-mat.quant-gas↗

arXiv2014

The one-dimensional Bose-Fermi-Hubbard model in the ultrafast-fermion limit: Charge density wave phase and MI - CDW phase separation

In a recent work [1] we presented results for the Bose-Fermi-Hubbard model (BFHM) in the limit of ultrafast fermions. The present work gives an overview over the used methods and an deeper insight into the implications arising from the treated limit. Starting from the discussion of the phase diagram obtained by numerical means, we develop an analytic theory and derive an effective bosonic Hamiltonian. Arising issues in the Hamiltonian are overcome by inclusion of a back-action, renormalizing the solution of our system. Based on a detailed analysis of the effective Hamiltonian, the phase diagram in the thermodynamic limit is constructed by analytic means and comparison to numerical results obtained by density matrix renormalization group (DMRG) techniques for the full BFHM shows a very reasonable agreement. 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 with inclusion of important effects due to the boundary condition.

cond-mat.quant-gas↗

arXiv2011

Multi-band and nonlinear hopping corrections to the 3D Bose-Fermi Hubbard model

Recent experiments revealed the importance of higher-band effects for the Mott insulator (MI) -- superfluid transition (SF) of ultracold bosonic atoms or mixtures of bosons and fermions in deep optical lattices [Best \emph{et al.}, PRL \textbf{102}, 030408 (2009); Will \emph{et al.}, Nature \textbf{465}, 197 (2010)]. In the present work, we derive an effective lowest-band Hamiltonian in 3D that generalizes the standard Bose-Fermi Hubbard model taking these effects as well as nonlinear corrections of the tunneling amplitudes mediated by interspecies interactions into account. It is shown that a correct description of the lattice states in terms of the bare-lattice Wannier functions rather than approximations such as harmonic oscillator states is essential. In contrast to self-consistent approaches based on effective Wannier functions our approach provides a quantitative explanation of the observed reduction of the superfluid phase for repulsive interspecies interactions.

cond-mat.quant-gas↗

arXiv2009

Fermion mediated long-range interactions of bosons in the 1D Bose-Fermi-Hubbard model

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 besides bosonic Mott insulating (MI), superfluid (SF), and charge density-wave phases (CDW) a novel 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 the interplay between fermion-induced mean-field potential and long range interaction with alternating sign.

cond-mat.other↗

arXiv2009

Analytic approximations to the phase diagram of the Jaynes-Cummings-Hubbard model with application to ion chains

We discuss analytic approximations to the ground state phase diagram of the homogeneous Jaynes-Cummings-Hubbard (JCH) Hamiltonian with general short-range hopping. The JCH model describes e.g. radial phonon excitations of a linear chain of ions coupled to an external laser field tuned to the red motional sideband with Coulomb mediated hopping or an array of high-$Q$ coupled cavities containing a two-level atom and photons. Specifically we consider the cases of a linear array of coupled cavities and a linear ion chain. We derive approximate analytic expressions for the boundaries between Mott-insulating and superfluid phases and give explicit expressions for the critical value of the hopping amplitude within the different approximation schemes. In the case of an array of cavities, which is represented by the standard JCH model we compare both approximations to numerical data from density-matrix renormalization group (DMRG) calculations.

cond-mat.other↗