Bosonization study of a generalized statistics model with four Fermi points

We study a one-dimensional lattice model of fractional statistics in which particles have next-nearest-neighbor hopping between sites depends on the occupation number at intermediate site and statistical parameter $\phi$. The breaks parity time-reversal symmetries has four-fermion interactions if $\phi \ne 0$. first analyze using mean field theory find that there are four Fermi points whose locations depend $\phi$ filling $\eta$. then modes near technique bosonization. Based quadratic terms bosonized Hamiltonian, we low-energy form two decoupled Tomonaga-Luttinger liquids with different values Luttinger parameters $\eta$; further, right left moving each system velocities. A scaling dimensions cosine Hamiltonian indicates appearing one will flow under renormalization group may reach non-trivial fixed point long distance limit. examine various charge density superconducting order to them is most relevant for Finally look two-particle bound states appear this discuss their possible relevance properties thermodynamic Our work shows rich structure as function