Symmetry Enriched Criticality from Kennedy Tasaki Self-Duality
Abstract
The interplay between topology and quantum criticality has established symmetry enriched criticality as a new paradigm beyond conventional frameworks in condensed matter and statistical physics. However, the conditions under which such criticality emerges remain poorly understood. In this work, we show that a broad class of symmetry enriched critical points separating symmetry protected topological (SPT) and spontaneous symmetry breaking (SSB) phases is governed by Kennedy Tasaki (KT) self duality. At these criticalities, the KT transformation that interchanges the SPT and SSB phases acts as a self-dual noninvertible symmetry, endowing the critical points with nontrivial topological characteristics. We numerically demonstrate this mechanism in ℤn × ℤn cluster qudit chains and further argue that it naturally extends to higher dimensions, providing a duality based criterion for identifying symmetry-enriched criticality across dimensions.
Related
- Quantum quenches of scar states in the Affleck-Kennedy-Lieb-Tasaki model via Clifford augmented tensor network simulation
- Emergent Scaling Symmetry and Universal Interior Criticality of Scalarized Black Holes
- Interacting quantum criticality with U(1) symmetry breaking in 1+1 dimensions
- Collective Symmetry and Criticality from Single-Component Fluctuations
- Theory of criticality-enabled U(1) symmetry breaking in a class of 1+1D systems
BibTeX
@misc{chen2026symmetry,
title = {{Symmetry Enriched Criticality from Kennedy Tasaki Self-Duality}},
author = {Mingyuan Chen and Sheng Yang and Xue-Jia Yu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27666},
eprint = {2610.27666},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27666},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Symmetry Enriched Criticality from Kennedy Tasaki Self-Duality
AU - Mingyuan Chen
AU - Sheng Yang
AU - Xue-Jia Yu
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.27666
UR - https://arxiv.org/abs/2610.27666
AB - The interplay between topology and quantum criticality has established symmetry enriched criticality as a new paradigm beyond conventional frameworks in condensed matter and statistical physics. However, the conditions under which such criticality emerges remain poorly understood. In this work, we show that a broad class of symmetry enriched critical points separating symmetry protected topological (SPT) and spontaneous symmetry breaking (SSB) phases is governed by Kennedy Tasaki (KT) self duality. At these criticalities, the KT transformation that interchanges the SPT and SSB phases acts as a self-dual noninvertible symmetry, endowing the critical points with nontrivial topological characteristics. We numerically demonstrate this mechanism in ℤ_n × ℤ_n cluster qudit chains and further argue that it naturally extends to higher dimensions, providing a duality based criterion for identifying symmetry-enriched criticality across dimensions.
ER -