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arXiv · 2412.03793

Nonuniform Parafermion Chains: Low-Energy Physics and Finite-Size Effects

Mohammad Mahdi Nasiri Fatmehsari·Mohammad-Sadegh Vaezi
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Abstract

The nonuniform $\mathbb{Z}_2$ symmetric Kitaev chain, comprising alternating topological and normal regions, hosts localized states known as edge-zero modes (EZMs) at its interfaces. These EZMs can pair to form qubits that are resilient to quantum decoherence, a feature expected to extend to higher symmetric chains, i.e., parafermion chains. However, finite-size effects may impact this ideal picture. Diagnosing these effects requires first a thorough understanding of the low-energy physics where EZMs may emerge. Previous studies have largely focused on uniform chains, with nonuniform cases inferred from these results. While recent work [Narozhny, Sci. Rep. 7, 1447 (2017)] provides an insightful analytical solution for a nonuniform $\mathbb{Z}_2$ chain with two topological regions separated by a normal one, its complexity limits its applicability to chains with more regions or higher symmetries. Here, we present a new approach based on decimating the highest-energy terms, facilitating the scalable analysis of $\mathbb{Z}_n$ chains with any number of regions. We provide analytical results for both $\mathbb{Z}_2$ and$\mathbb{Z}_3$ chains, supported by numerical findings, and identify the critical lengths necessary to preserve well-separated EZMs.

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Mohammad Mahdi Nasiri Fatmehsari, Mohammad-Sadegh Vaezi. 2024-12-05. Nonuniform Parafermion Chains: Low-Energy Physics and Finite-Size Effects. https://doi.org/10.1038/s41598-025-94657-z

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