| We study a spin-½ chain in which spins are located on the vertices of the tetragons connected and exchange interact along links. The model presented has exact solution for an arbitrary value of the exchange integral. The ground state phase diagram consists of two topological phases with different static Z2 gauge fields, all Z2 charges are equal to +1 or -1. The vortex-free field configurations satisfy flat-band or gapless-band single particle spectrum of the Majorana fermions in the chain. We find that at critical value of the exchange integral Jc=0.49 the phase transition between topological phases in this many-body system induces a metal-insulator phase transition with an essential spectrum rearrangement. We also give detailed analysis of the zero-temperature phase diagram of the model and demonstrate how this unusual behavior of the metal-insulator transition with a spectrum rearrangement arises. |
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