TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.18.3.094
TI  - Pivoting through the chiral-clock family
PY  - 2025/03/14
UR  - https://scipost.org/SciPostPhys.18.3.094
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 18
IS  - 3
SP  - 094
A1  - Jones, Nick
AU  - Prakash, Abhishodh
AU  - Fendley, Paul
AB  - The Onsager algebra, invented to solve the two-dimensional Ising model, can be used to construct conserved charges for a family of integrable $N$-state chiral clock models. We show how it naturally gives rise to a "pivot" procedure for this family of chiral Hamiltonians. These Hamiltonians have an anti-unitary CPT symmetry that when combined with the usual $\mathbb{Z}_N$ clock symmetry gives a non-Abelian dihedral symmetry group $D_{2N}$. We show that this symmetry gives rise to symmetry-protected topological (SPT) order in this family for all even $N$, and representation-SPT (RSPT) physics for all odd $N$. The simplest such example is a next-nearest-neighbour chain generalising the spin-1/2 cluster model, an SPT phase of matter. We derive a matrix-product state representation of its fixed-point ground state along with the ensuing entanglement spectrum and symmetry fractionalisation. We analyse a rich phase diagram combining this model with the Onsager-integrable chiral Potts chain, and find trivial, symmetry-breaking and (R)SPT orders, as well as extended gapless regions. For odd $N$, the phase transitions are "unnecessarily" critical from the SPT point of view.
ER  -

@Article{10.21468/SciPostPhys.18.3.094,
	title={{Pivoting through the chiral-clock family}},
	author={Nick G. Jones and Abhishodh Prakash and Paul Fendley},
	journal={SciPost Phys.},
	volume={18},
	pages={094},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.18.3.094},
	url={https://scipost.org/10.21468/SciPostPhys.18.3.094},
}