Effect of slowly decaying long-range interactions on topological qubits
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915937487159296 |
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| author | Granet, Etienne Levin, Michael |
| author_facet | Granet, Etienne Levin, Michael |
| contents | We study the robustness of topological ground state degeneracy to long-range interactions in quantum many-body systems. We focus on slowly decaying two-body interactions that scale like a power-law $1/r^α$ where $α$ is smaller than the spatial dimension; such interactions are beyond the reach of known stability theorems which only apply to short-range or rapidly decaying long-range perturbations. Our main result is a computation of the ground state splitting of several toy models, which are variants of the 1D Ising model $H = -\sum_i σ^z_i σ^z_{i+1} + λ\sum_{ij} |i-j|^{-α} σ^x_i σ^x_j$ with $λ> 0$ and $α< 1$. In one variant, the power-law interactions are replaced by all-to-all interactions, $\fracλ{4 L^α}\sum_{ij} σ^x_i σ^x_j$, where $L$ is the system size, while the other variant has true power-law interactions but is built out of quantum rotors rather than Ising spins. These models are also closely connected to the Kitaev p-wave wire model with power-law density-density interactions. In these examples, we find that the splitting $δ$ scales like a stretched exponential $δ\sim \exp(-C L^{\frac{1+α}{2}})$.
Our computations are based on path integral techniques similar to the instanton method introduced by Coleman. We also study another toy model with long-range interactions that can be analyzed without path integral techniques and that shows similar behavior. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_02809 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Effect of slowly decaying long-range interactions on topological qubits Granet, Etienne Levin, Michael Quantum Physics We study the robustness of topological ground state degeneracy to long-range interactions in quantum many-body systems. We focus on slowly decaying two-body interactions that scale like a power-law $1/r^α$ where $α$ is smaller than the spatial dimension; such interactions are beyond the reach of known stability theorems which only apply to short-range or rapidly decaying long-range perturbations. Our main result is a computation of the ground state splitting of several toy models, which are variants of the 1D Ising model $H = -\sum_i σ^z_i σ^z_{i+1} + λ\sum_{ij} |i-j|^{-α} σ^x_i σ^x_j$ with $λ> 0$ and $α< 1$. In one variant, the power-law interactions are replaced by all-to-all interactions, $\fracλ{4 L^α}\sum_{ij} σ^x_i σ^x_j$, where $L$ is the system size, while the other variant has true power-law interactions but is built out of quantum rotors rather than Ising spins. These models are also closely connected to the Kitaev p-wave wire model with power-law density-density interactions. In these examples, we find that the splitting $δ$ scales like a stretched exponential $δ\sim \exp(-C L^{\frac{1+α}{2}})$. Our computations are based on path integral techniques similar to the instanton method introduced by Coleman. We also study another toy model with long-range interactions that can be analyzed without path integral techniques and that shows similar behavior. |
| title | Effect of slowly decaying long-range interactions on topological qubits |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2512.02809 |