We study a model of strongly correlated spinless fermions on a kagome lattice at 1/3 filling, with interactions described by an extended Hubbard Hamiltonian. An effective Hamiltonian in the desired strong correlation regime is derived, from which the spectral functions are calculated by means of exact diagonalization techniques. We present our numerical results with a view to discussion of possible signatures of confinement/deconfinement of fractional charges.

We discuss the metal-insulator transition of the spinless fermion model on a kagome lattice at 1/3 filling. The system is analyzed by using exact diagonalization, density-matrix renormalization group methods, and random-phase approximation. In the strong-coupling region, the charge-ordered ground state is consistent with the predictions of an effective model, i.e., plaquette order. We find that the qualitative properties of the metal-insulator transition are totally different depending on the sign of the hopping matrix elements, reflecting the difference in the band structure near the Fermi level.

We use the multiscale entanglement renormalisation ansatz (MERA) to numerically investigate three critical quantum spin chains with Z2 × Z2 on-site symmetry: a staggered XXZ model, a transverse field cluster model, and the quantum Ashkin-Teller model. All three models possess a continuous one-parameter family of critical points. Along this critical line, the thermodynamic limit of these models is expected to be described by classes of c = 1 conformal field theories (CFTs) of two possible types: the S 1 free boson and its Z2-orbifold. Our numerics using MERA with explicitly enforced Z2 × Z2 symmetry allow us to extract conformal data for each model, with strong evidence supporting the identification of the staggered XXZ model and critical transverse field cluster model with the S 1 boson CFT, and the Ashkin-Teller model with the Z2-orbifold boson CFT. Our first two models describe the phase transitions between symmetry protected topologically ordered phases and trivial phases, which lie outside the usual Landau-Ginsburg-Wilson paradigm of symmetry breaking. Our results show that a range of critical theories can arise at the boundary of a single symmetry protected phase. arXiv:1501.02817v2 [cond-mat.str-el]