Strongly correlated flat-band systems: Ground state and low-temperature properties

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Strongly correlated flat-band systems may exhibit interesting phenomena such as Wigner crystallization, high-temperature fractional quantum Hall states, macroscopic magnetization jumps, or magnetic-field induced spin-Peierls instabilities. Moreover, they provide a route to ferromagnetism in the Hubbard model. In this project, we consider a class of strongly correlated frustrated systems with a completely dispersionless (flat) one-particle band (flat-band systems), for which exact many-body localized ground states can be constructed. The corresponding low-energy degrees of freedom of the quantum model can be described by classical lattice-gas models. We apply this concept on quantum spin systems described by the Heisenberg model as well as on electron systems described by the Hubbard model. The effective classical lattice-gas models can be used to calculate the low-temperature thermodynamics of the corresponding quantum models. For Hubbard systems the localized states lead to ground-state ferromagnetism which can be considered as a Pauli correlated percolation problem. The relaxation of the flat-band condition may lead to new quantum effects.