Estimating entanglement in 2D Heisenberg model in the strong rung-coupling limit
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866912058883178496 |
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| author | Pushpan, Chandrima B. J., Harikrishnan K. Narayan, Prithvi Pal, Amit Kumar |
| author_facet | Pushpan, Chandrima B. J., Harikrishnan K. Narayan, Prithvi Pal, Amit Kumar |
| contents | In this paper, we calculate entanglement in the isotropic Heisenberg model in a magnetic field on a two-dimensional rectangular zig-zag lattice in the strong rung-coupling limit, using the one-dimensional XXZ model as a proxy. Focusing on the leading order in perturbation, for arbitrary size of the lattice, we show how the one-dimensional effective description emerges. We point out specific states in the low-energy sector of the two-dimensional model that are well-approximated by the one-dimensional spin-1/2 XXZ model. We propose a systematic approach for mapping matrix-elements of operators defined on the two-dimensional model to their low-energy counterparts on the one-dimensional XXZ model. We also show that partial trace-based description of entanglement in the two-dimensional model can be satisfactorily approximated using the one-dimensional XXZ model as a substitute. We further show numerically that the one-dimensional XXZ model performs well in estimating entanglement quantified using a measurement-based approach in the two-dimensional model for specific choices of measured Hermitian operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_04615 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Estimating entanglement in 2D Heisenberg model in the strong rung-coupling limit Pushpan, Chandrima B. J., Harikrishnan K. Narayan, Prithvi Pal, Amit Kumar Quantum Physics Strongly Correlated Electrons In this paper, we calculate entanglement in the isotropic Heisenberg model in a magnetic field on a two-dimensional rectangular zig-zag lattice in the strong rung-coupling limit, using the one-dimensional XXZ model as a proxy. Focusing on the leading order in perturbation, for arbitrary size of the lattice, we show how the one-dimensional effective description emerges. We point out specific states in the low-energy sector of the two-dimensional model that are well-approximated by the one-dimensional spin-1/2 XXZ model. We propose a systematic approach for mapping matrix-elements of operators defined on the two-dimensional model to their low-energy counterparts on the one-dimensional XXZ model. We also show that partial trace-based description of entanglement in the two-dimensional model can be satisfactorily approximated using the one-dimensional XXZ model as a substitute. We further show numerically that the one-dimensional XXZ model performs well in estimating entanglement quantified using a measurement-based approach in the two-dimensional model for specific choices of measured Hermitian operators. |
| title | Estimating entanglement in 2D Heisenberg model in the strong rung-coupling limit |
| topic | Quantum Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2301.04615 |