Nonuniform Parafermion Chains: Low-Energy Physics and Finite-Size Effects
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| Format: | Preprint |
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2024
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| _version_ | 1866918012456534016 |
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| author | Fatmehsari, Mohammad Mahdi Nasiri Vaezi, Mohammad-Sadegh |
| author_facet | Fatmehsari, Mohammad Mahdi Nasiri Vaezi, Mohammad-Sadegh |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_03793 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonuniform Parafermion Chains: Low-Energy Physics and Finite-Size Effects Fatmehsari, Mohammad Mahdi Nasiri Vaezi, Mohammad-Sadegh Strongly Correlated Electrons Mesoscale and Nanoscale Physics Statistical Mechanics Superconductivity Quantum Physics 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. |
| title | Nonuniform Parafermion Chains: Low-Energy Physics and Finite-Size Effects |
| topic | Strongly Correlated Electrons Mesoscale and Nanoscale Physics Statistical Mechanics Superconductivity Quantum Physics |
| url | https://arxiv.org/abs/2412.03793 |