A Fractional Chiral Semimetal

Formulating consistent theories describing strongly correlated metallic topological phases is an outstanding problem in condensed matter physics I will present an explicit construction of a fractionalized analog of the Weyl semimetal state: the fractional chiral metal Our approach is to construct a 4 1D quantum Hall insulator by stacking 3 1D Weyl semimetals in a magnetic field In a strong enough field the low energy physics is determined by the lowest Landau level of each Weyl semimetal which is highly degenerate and chiral motivating us to use a coupled wire approach In the presence of electron electron interactions a gapped phase emerges its electromagnetic response is given in terms of a Chern Simons field theory A boundary of this four dimensional phase remains gapless The boundary s response to an external electromagnetic field is determined by a chiral anomaly with a fractional coefficient We suggest that such an anomalous response can be taken as a working definition of a fractionalized strongly correlated analog of the Weyl semimetal state