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A construction of exotic metallic states

We discuss examples of two dimensional metallic states with charge fractionalization, and we will demonstrate that the mechanism of charge fractionalization leads to exotic metallic behaviors at low and intermediate temperature. The simplest example of such state is constructed by fermionic partons at finite density coupled to a $Z_N$ gauge field, whose properties can be studied through rudimentary methods. This simple state has the following exotic features: (1) at low temperature this state is a "bad metal" whose resistivity can exceed the Mott-Ioffe-Regel limit; (2) while increasing temperature $T$ the resistivity $ρ(T)$ is a nonmonotonic function, and it crosses over from a bad metal at low $T$ to a good metal at relatively high $T$; (3) the optical conductivity $σ(ω)$ has a small Drude weight at low $T$, and a larger Drude weight at intermediate $T$; (4) at low temperature the metallic state has a large Lorenz number, which strongly violates the Wiedemann-Franz law. A more complex example with fermionic partons at finite density coupled to a SU(N) gauge field will also be constructed.