Tune the dynamics generated by the excitable zero-mode manifold

Determine to what extent the dynamics generated by excitable zero-modes in the one-dimensional star-lattice PXP model can be tuned through the choice of the auxiliary matrices A and B.

Background

The one-dimensional star-lattice PXP model supports a continuous matrix-product-state manifold of excitable zero-modes. Under open boundary conditions, suitable boundary vectors produce eigenstates at energies 0 and ±√3, while boundary vectors with support in both auxiliary sectors generate indefinitely oscillating states.

The paper identifies the matrices A and B as continuous parameters of the MPS construction, but does not determine the range of dynamical behaviors accessible by varying them. Establishing how these parameters control observables, oscillation amplitudes, entanglement, or other dynamical signatures is therefore left unresolved.

References

While the dynamics that can be engineered using the EZMs has been briefly discussed in Section~\ref{sec:dyn}, there remains much to be studied. In particular, to what extent the dynamics can be tuned using the $A$ and $B$ matrices is a promising future direction of research.

— Efficient search for excitable zero-modes in constrained systems  (2608.31165 - Desaules, 31 Aug 2026) in Section 3.3, Conclusion

It would also be interesting to further study the remaining ZMs which could not be explained through the local eigenstate approach for $L_\Delta$ even. While these are likely not excitable (see also Appendix~\ref{app:cg}), they could still have some tractable structure.

— Efficient search for excitable zero-modes in constrained systems  (2608.31165 - Desaules, 31 Aug 2026) in Section 3.3, Conclusion