Ginzberg-Landau-Wilson theory for flat band, Fermi-arc and surface states of strongly correlated systems

We show that we can realize the surface state together with the bulk state of various types of topological matters in holographic context, by considering various types of Lorentz symmetry breaking. The fermion spectral functions in the presence of order show features like the gap, pseudo-gap, flat disk bands and the Fermi-arc connecting the two Dirac cones, which are familiar in Weyl and Dirac materials or Kondo lattice. Many of above features are associated with the zero modes whose presence is tied with a discrete symmetry of the interaction and these zero modes are associated with the surface states. Some of the order parameters in the bulk theory do not have an interpretation of symmetry breaking in terms of the boundary space, which opens the possibility of ‘an order without symmetry breaking’. We also pointed out that the spectrum of the symmetry broken phase mimics that of weakly interacting theory, although their critical version describe the strongly interacting system.