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Abstract:

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.

Abstract:

SciPost Submission Detail Pivoting through the chiral-clock family

Abstract:

We introduce an SU⁡(𝑀)-symmetric disordered bipartite spin model with unusual characteristics. Although superficially similar to the Sachdev-Ye (SY) model, it has several markedly different properties for 𝑀≥3. In particular, it has a large nontrivial nullspace whose dimension grows exponentially with system size. The states in this nullspace are frustration-free and are ground states when the interactions are ferromagnetic. The exponential growth of the nullspace leads to Hilbert-space fragmentation and a violation of the eigenstate thermalization hypothesis. We demonstrate that the commutant algebra responsible for this fragmentation is a nontrivial subalgebra of the Read-Saleur commutant algebra of certain nearest-neighbor models such as the spin-1 biquadratic spin chain. We also discuss the low-energy behavior of correlations for the disordered version of this model in the limit of a large number of spins and large 𝑀, using techniques similar to those applied to the SY model. We conclude by generalizing the Shiraishi-Mori embedding formalism to nonlocal models, and apply it to turn some of our nullspace states into quantum many-body scars.