Enforced Gaplessness by Combining Non-Anomalous Symmetries
Abstract
Symmetry-enforced gaplessness is a phenomenon in which a quantum system is forced to be gapless due to its global symmetry. Previous works have mainly focused on anomalous symmetries. Another approach, using symmetry spans, which specify two embeddings of a common symmetry into two larger symmetries, was proposed by the authors. In this work, we show that a symmetry span can enforce gaplessness even when both larger symmetries are invertible and non-anomalous: each alone admits a trivially gapped phase, but because the embeddings differ by a twist associated with a symmetry-protected topological phase, the symmetry they generate admits no gapped phase with finitely many ground states. We present such a span of a finite group and U(1)2 in 1+1 dimensions, with continuum realizations and a lattice Hamiltonian, with a finite-dimensional local Hilbert space and finitely many parameters, that is gapless in any region of its parameter space. We also discuss a 2+1-dimensional example and spans of only finite symmetries.
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BibTeX
@misc{ando2026enforced,
title = {{Enforced Gaplessness by Combining Non-Anomalous Symmetries}},
author = {Takamasa Ando and Kantaro Ohmori},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03164},
eprint = {2611.03164},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03164},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Enforced Gaplessness by Combining Non-Anomalous Symmetries
AU - Takamasa Ando
AU - Kantaro Ohmori
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03164
UR - https://arxiv.org/abs/2611.03164
AB - Symmetry-enforced gaplessness is a phenomenon in which a quantum system is forced to be gapless due to its global symmetry. Previous works have mainly focused on anomalous symmetries. Another approach, using symmetry spans, which specify two embeddings of a common symmetry into two larger symmetries, was proposed by the authors. In this work, we show that a symmetry span can enforce gaplessness even when both larger symmetries are invertible and non-anomalous: each alone admits a trivially gapped phase, but because the embeddings differ by a twist associated with a symmetry-protected topological phase, the symmetry they generate admits no gapped phase with finitely many ground states. We present such a span of a finite group and U(1)^2 in 1+1 dimensions, with continuum realizations and a lattice Hamiltonian, with a finite-dimensional local Hilbert space and finitely many parameters, that is gapless in any region of its parameter space. We also discuss a 2+1-dimensional example and spans of only finite symmetries.
ER -