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Strongly correlated electrons : from two dimensions to heterostructures

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Figure 1.3: k -points in the rst Brillouin zone of a N = 6 × 6 square lat- lat-tice. The four types of symbols specify the type of boundary condition (b x , b y ) chosen, b α = 0 corresponding to periodic BC and b α = 1 to anti-periodic BC.
Figure 1.4: On a N = 8 × 8 cluster, symmetries lead to highly degenerate spectra with only few peaks (continuous line)
Figure 2.1: Phase diagram of the ionic Hubbard model as obtained from DQMC simulations
Figure 2.2: Non-interacting dispersion relation of the Hubbard bilayer with opposite in-layer hopping signs
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