Variational Minimization of Almost Strong Zero Modes in Parafermionic Wires
Abstract
Strongly interacting fermionic chains obeying a Zn symmetry can host topological phases with highly degenerate ground-state manifolds. The different ground states are connected by strongly bound fractionalized edge modes called parafermionic zero modes. While exactly preserved under time evolution at zero temperature, interactions lead to a destabilization of these modes at finite energy densities, and, given a generic Hamiltonian, obtaining the lifetime of these modes is often impossible as it requires knowledge of the full spectrum of the Hamiltonian or long time evolutions. Here, we propose a novel quantum-inspired algorithm that can be used to variationally search for these almost strong zero modes in generic parafermionic chain models. We demonstrate analytically and numerically that our ansatz faithfully reproduces the exact results and finds strongly bound parafermionic operators in the non-integrable Kitaev-Hubbard chain and chiral Potts model. Our results further allow us to verify the existence of a true strong zero mode in the symmetrical limit of the chiral Potts model for Z3-parafermions.
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BibTeX
@misc{tausendpfund2026variational,
title = {{Variational Minimization of Almost Strong Zero Modes in Parafermionic Wires}},
author = {Niklas Tausendpfund and Matteo Rizzi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15748},
eprint = {2610.15748},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15748},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Variational Minimization of Almost Strong Zero Modes in Parafermionic Wires
AU - Niklas Tausendpfund
AU - Matteo Rizzi
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.15748
UR - https://arxiv.org/abs/2610.15748
AB - Strongly interacting fermionic chains obeying a Z_n symmetry can host topological phases with highly degenerate ground-state manifolds. The different ground states are connected by strongly bound fractionalized edge modes called parafermionic zero modes. While exactly preserved under time evolution at zero temperature, interactions lead to a destabilization of these modes at finite energy densities, and, given a generic Hamiltonian, obtaining the lifetime of these modes is often impossible as it requires knowledge of the full spectrum of the Hamiltonian or long time evolutions. Here, we propose a novel quantum-inspired algorithm that can be used to variationally search for these almost strong zero modes in generic parafermionic chain models. We demonstrate analytically and numerically that our ansatz faithfully reproduces the exact results and finds strongly bound parafermionic operators in the non-integrable Kitaev-Hubbard chain and chiral Potts model. Our results further allow us to verify the existence of a true strong zero mode in the symmetrical limit of the chiral Potts model for Z_3-parafermions.
ER -