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arXiv · 2301.04615

Estimating entanglement in 2D Heisenberg model in the strong rung-coupling limit

Chandrima B. Pushpan·Harikrishnan K. J.·Prithvi Narayan·Amit Kumar Pal
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Abstract

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.

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Chandrima B. Pushpan, Harikrishnan K. J., Prithvi Narayan, Amit Kumar Pal. 2023-01-11. Estimating entanglement in 2D Heisenberg model in the strong rung-coupling limit. https://doi.org/10.1103/physreva.110.032408

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