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The properties of a phase at finite interactions can be significantlyinfluenced by the underlying dispersion of the non-interacting Hamiltonian. Wedemonstrate this by studying the repulsive Hubbard model on the $2$D Lieblattice, which has a flat band for vanishing interaction $U$. We performreal-space dynamical mean-field theory calculations at different temperaturesand dopings using a continuous time quantum Monte Carlo impurity solver.Studying the frequency dependence of the self-energy, we show that a finitetemperature non-magnetic non-Fermi liquid behavior is a concomitant of the flatband singularity. At half-filling we also find a magnetically ordered region,where the order parameter varies linearly with the interaction strength, and astrongly correlated Mott insulating phase. The double occupancy decreasessharply for small $U$, highlighting the flat band contribution. Away fromhalf-filling, we observe the stripe order, i.e. an inhomogeneous spin andcharge density wave of finite wavelength which turns into a sub-latticeordering at higher temperatures.

Temperature and doping induced instabilities of the repulsive Hubbard model on Lieb lattice