Holographic Representations of Topological Quantum Criticality: Emergent Symmetry Approach around the Bott Clock
Abstract
In this article, we apply the idea of emergent symmetries to construct holographic representations of a broad class of topological quantum critical points (tQCPs) that appear in fermionic classes in the Bott clock. We show explicitly that around the Bott clock, an emergent symmetry UEM exists at a tQCP between different symmetry protected gapped phases with protecting symmetry Gp in d spatial dimensions. This emergent symmetry can be used to construct a (d+1) spatial dimensional lattice model with a properly upgraded symmetry such as UEM× Gp or UEM rtimes Gp, etc. By doubling the degrees of freedom of the adjacent topological class in d-dimensions, we successfully show that the (d+1)-dimensional lattice models constructed in this way have the desired enlarged symmetry groups that precisely belong to the adjacent topological classes, counterclockwise around the Bott clock. Furthermore, d-dimensional boundaries of these (d+1) dimensional lattice models of gapped topological classes are shown to exhibit identical infrared dynamics as the corresponding tQCPs in the d-dimensional adjacent topological phases in the Bott clock, with lower symmetries.
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BibTeX
@misc{yang2026holographic,
title = {{Holographic Representations of Topological Quantum Criticality: Emergent Symmetry Approach around the Bott Clock}},
author = {Fan Yang and Fei Zhou},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.30335},
eprint = {2608.30335},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30335},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Holographic Representations of Topological Quantum Criticality: Emergent Symmetry Approach around the Bott Clock
AU - Fan Yang
AU - Fei Zhou
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.30335
UR - https://arxiv.org/abs/2608.30335
AB - In this article, we apply the idea of emergent symmetries to construct holographic representations of a broad class of topological quantum critical points (tQCPs) that appear in fermionic classes in the Bott clock. We show explicitly that around the Bott clock, an emergent symmetry U_EM exists at a tQCP between different symmetry protected gapped phases with protecting symmetry G_p in d spatial dimensions. This emergent symmetry can be used to construct a (d+1) spatial dimensional lattice model with a properly upgraded symmetry such as U_EM× G_p or U_EM rtimes G_p, etc. By doubling the degrees of freedom of the adjacent topological class in d-dimensions, we successfully show that the (d+1)-dimensional lattice models constructed in this way have the desired enlarged symmetry groups that precisely belong to the adjacent topological classes, counterclockwise around the Bott clock. Furthermore, d-dimensional boundaries of these (d+1) dimensional lattice models of gapped topological classes are shown to exhibit identical infrared dynamics as the corresponding tQCPs in the d-dimensional adjacent topological phases in the Bott clock, with lower symmetries.
ER -