Charge-density-wave phases of one-dimensional model with long-range repulsive interactions
The one-dimensional extended t-V model on a lattice describes fermions with repulsive interactions of finite range and exhibits a quantum phase transition between a Luttinger liquid conducting phase and a Mott insulating phase. Its properties make it useful in the description of candidate materials for Mott transistor devices. It is known that by tailoring the potential energy of the insulating system, one can force a phase transition into a different insulating phase [1, 2]. We show how to construct all possible charge-density-wave phases of the system at low critical densities in the atomic limit. Higher critical densities are investigated by a brute-force analysis of the possible finite unit cells of the Fock states. We present example phase diagrams of the system.
We construct a matrix product operator representation of the Hamiltonian of the t-V model. Using the matrix product states (MPS) approach we go beyond the atomic limit, where the phase diagrams are much richer. MPS method is especially problematic near the transition between two different charge-density-wave phases and we show how the bond dimension must be increased in order to converge the results.
Our results indicate that the number of possible insulating phases grows with both the maximum interaction range and the fermion density and may cause the loss of insulating properties of the material at finite temperatures.
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