Topological Luttinger Liquids from Decorated Domain Walls

TL;DR

This paper constructs a new class of gapless symmetry protected topological phases in one dimension by decorating domain walls of Luttinger liquids, revealing novel boundary critical behavior and robust edge modes.

Contribution

It introduces a systematic method to create gapless SPT phases in 1D by decorating domain walls, with detailed boundary analysis and numerical validation.

Findings

Boundary critical behavior differs from conventional Luttinger liquids.

Robust symmetry-protected edge modes are demonstrated.

Numerical results confirm theoretical predictions.

Abstract

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.