Abstract
It is shown that three-dimensional systems of coupled quantum wires support fractional topological phases composed of closed loops and open planes of two-dimensional fractional quantum Hall subsystems. These phases have topologically protected edge states, and are separated by exotic quantum phase transitions corresponding to a rearrangement of fractional quantum Hall edge modes. Some support for the existence of an extended exotic critical phase separating the bulk gapped fractional topological phases is given. Without electron-electron interactions, similar but unfractionalized bulk gapped phases based on coupled integer quantum Hall states exist. They are separated by an extended critical Weyl semimetal phase.
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