A novel hierarchy of the one-dimensional SU(N) electron models with 1/ ${\mathit{r}}^{2}$ interaction is proposed and solved by the asymptotic Bethe ansatz both for the continuum and lattice cases. The construction of the hierarchy is closely related to that for the fractional quantum Hall effect (FQHE) of the filling factor ${\ensuremath{\nu}}_{\mathit{c}}$=1/[ ${\mathit{p}}_{1}$ -1/( ${\mathit{p}}_{2}$ -...-1/ ${\mathit{p}}_{\mathit{N}}$ )...]. Under the chiral constraint the model describes the essential properties of the edge states for the FQHE with the above filling fraction. Furthermore the matrix deduced from the excitation spectrum characterizes the topological order of the FQHE state.A novel hierarchy of the one-dimensional SU(N) electron models with 1/${\mathit{r}}^{2}$ interaction is proposed and solved by the asymptotic Bethe ansatz both for the continuum and lattice cases. The construction of the hierarchy is closely related to that for the fractional quantum Hall effect (FQHE) of the filling factor ${\ensuremath{\nu}}_{\mathit{c}}$=1/[${\mathit{p}}_{1}$-1/(${\mathit{p}}_{2}$-...-1/${\mathit{p}}_{\mathit{N}}$)...]. Under the chiral constraint the model describes the essential properties of the edge states for the FQHE with the above filling fraction. Furthermore the matrix deduced from the excitation spectrum characterizes the topological order of the FQHE state.

Physical Review LettersJul 12, 199350 citations

A novel hierarchy of the one-dimensional SU(N) electron models with 1/

{\mathit{r}}^{2}

interaction is proposed and solved by the asymptotic Bethe ansatz both for the continuum and lattice cases. The construction of the hierarchy is closely related to that for the fractional quantum Hall effect (FQHE) of the filling factor ${\ensuremath{\nu}}_{\mathit{c}}$=1/[

{\mathit{p}}_{1}

-1/(

{\mathit{p}}_{2}

-...-1/

{\mathit{p}}_{\mathit{N}}

)...]. Under the chiral constraint the model describes the essential properties of the edge states for the FQHE with the above filling fraction. Furthermore the matrix deduced from the excitation spectrum characterizes the topological order of the FQHE state.