An Intrinsically Gapless Topological Phase with Dipole Symmetry
Abstract
We show that the boundary fractionalization familiar from gapped topological insulators can enforce bulk gaplessness in a dipole-conserving system. In a one-dimensional fermion model with charge conservation, dipole conservation, and particle-hole symmetry, we realize an intrinsically gapless symmetry-protected topological (igSPT) phase combining a dipolar Luttinger liquid with half-quantized boundary charges. This boundary structure obstructs a unique gapped bulk preserving these symmetries and lattice translation. Remarkably, the two charge-neutral edge configurations remain exactly degenerate even at finite size due to dipole conservation and particle-hole symmetry. The boundary fractionalization also manifests as shifted conformal towers in the dipole-resolved entanglement spectrum, reflecting distinct conformal boundary conditions of the Luttinger liquid. We support our analysis of the igSPT by studying exactly-solvable limits and performing DMRG computations, establishing its stability for a wide range of tuning parameters.
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BibTeX
@misc{anakru2026intrinsically,
title = {{An Intrinsically Gapless Topological Phase with Dipole Symmetry}},
author = {Amogh Anakru and Linhao Li and Zhen Bi},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03538},
eprint = {2611.03538},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03538},
}
RIS
TY - UNPB
TI - An Intrinsically Gapless Topological Phase with Dipole Symmetry
AU - Amogh Anakru
AU - Linhao Li
AU - Zhen Bi
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03538
UR - https://arxiv.org/abs/2611.03538
AB - We show that the boundary fractionalization familiar from gapped topological insulators can enforce bulk gaplessness in a dipole-conserving system. In a one-dimensional fermion model with charge conservation, dipole conservation, and particle-hole symmetry, we realize an intrinsically gapless symmetry-protected topological (igSPT) phase combining a dipolar Luttinger liquid with half-quantized boundary charges. This boundary structure obstructs a unique gapped bulk preserving these symmetries and lattice translation. Remarkably, the two charge-neutral edge configurations remain exactly degenerate even at finite size due to dipole conservation and particle-hole symmetry. The boundary fractionalization also manifests as shifted conformal towers in the dipole-resolved entanglement spectrum, reflecting distinct conformal boundary conditions of the Luttinger liquid. We support our analysis of the igSPT by studying exactly-solvable limits and performing DMRG computations, establishing its stability for a wide range of tuning parameters.
ER -