Topological Luttinger Liquids from Decorated Domain Walls

Understand

We introduce a systematic construction of a gapless symmetry protected topological phase in one dimension by "decorating" the domain walls of Luttinger liquids.

• The resulting strongly interacting phases provide a concrete example of a gapless symmetry protected topological (gSPT) phase with robust symmetry-protected edge modes.
• Using boundary conformal field theory arguments, we show that while the bulks of such gSPT phases are identical to conventional Luttinger liquids, their boundary critical behavior is controlled by a different, strongly-coupled renormalization group fixed point.
• Our results are checked against extensive density matrix renormalization group calculations.