Bose condensation in flat bands

By Sebastian D. Huber, E. Altman. 2010

168 citations recorded by the source corpus.

We derive effective Hamiltonians for lattice bosons with strong geometrical frustration of the kinetic energy by projecting the interactions on the flat lowest Bloch band. Specifically, we consider the Bose Hubbard model on the one-dimensional sawtooth lattice and the two-dimensional kagome lattice. Starting from a strictly local interaction the projection gives rise to effective long-range terms stabilizing a supersolid phase at densities above ${\ensuremath{\nu}}_{c}=1/9$ of the kagome lattice. In the sawtooth lattice on the other hand we show that the solid order, which exists at the magic filling ${\ensuremath{\nu}}_{c}=1/4$, is unstable to further doping. The universal low-energy properties at filling $1/4+\ensuremath{\delta}\ensuremath{\nu}$ are described by the well-known commensurate-incommensurate transition. We support the analytic results by detailed numerical calculations using the density-matrix renormalization group and exact diagonalization. Finally, we discuss possible realizations of the models using ultracold atoms as well as frustrated quantum magnets in high magnetic fields. We compute the momentum distribution and the noise correlations, that can be extracted from time of flight experiments or neutron scattering, and point to signatures of the unique supersolid phase of the kagome lattice.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/9b2baea5e683de250d14d14792174a7abb30d726

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In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

Citations in the corpus

Topological bands for ultracold atoms (2018, unknown): “Such settings include the flat energy bands of frustrated lattices, such as the Creutz ladder (Creutz, 1999; Jünemann et al., 2017; Mazza et al., 2012) in 1D, and the Kagomé (Huber and Altman, 2010) and dice lattices (Möller and Cooper, 2012) in 2D, as well as for particles in dressed states of i”
Low-Disorder Microwave Cavity Lattices for Quantum Simulation with Photons (2012, background): “More recently there has been significant interest on studying the ground state of interacting bosons [49, 80, 106].”
Artificial flat band systems: from lattice models to experiments (2018, background): “When U > 1 the projected interaction is no longer local, but decays exponentially with distance if the flat band is gapped [47], and with a power law if a symmetry forces the flat band to touch a dispersive band edge [48].”