We discuss solutions of an algebraic model of the hexagonal lattice vibrations, which point out interesting localization properties of the eigenstates at van Hove singularities (vHs), whose energies correspond to Excited-State Quantum Phase Transitions (ESQPT). We show that these states form stripes oriented parallel to the zig-zag direction of the lattice, similar to the well-known edge states found at the Dirac point, however the vHs-stripes appear in the bulk. We interpret the states as lines of cell-tilting vibrations, and inspect their stability in the large lattice-size limit. The model can be experimentally realized by superconducting 2D microwave resonators containing triangular lattices of metallic cylinders, which simulate finite-sized graphene flakes. Thus we can assume that the effects discussed here could be experimentally observed.
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