Worldline deconfinement and emergent long-range interaction in the entanglement Hamiltonian and in the entanglement spectrum
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866913041274109952 |
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| author | Liu, Zenan Wang, Zhe Yao, Dao-Xin Yan, Zheng |
| author_facet | Liu, Zenan Wang, Zhe Yao, Dao-Xin Yan, Zheng |
| contents | The entanglement spectrum (ES) is a powerful tool for probing topological phases. While its behavior in gapped systems is well understood, its properties in gapless regimes remain unclear. In this work, we employ a quantum Monte Carlo method to study the ES of a two-dimensional square-octagon lattice Heisenberg model at quantum criticality and in the Néel phase. We find that the ES exhibits an M-shape magnon mode with a distinct sublinear dispersion, deviating from the conventional linear magnon. This behavior, similar to that of a one-dimensional long-range Heisenberg chain, reveals the emergence of relevant long-range interactions in the entanglement Hamiltonian. We demonstrate that the mechanism underlying short- and long-range interactions in the entanglement Hamiltonian can be interpreted as the confinement/deconfinement of worldlines in the path integral formulation. Our results reveal that gapless modes can fundamentally change the entanglement Hamiltonian and its spectrum, thereby offering insight into this general phenomenon. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_10078 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Worldline deconfinement and emergent long-range interaction in the entanglement Hamiltonian and in the entanglement spectrum Liu, Zenan Wang, Zhe Yao, Dao-Xin Yan, Zheng Strongly Correlated Electrons Statistical Mechanics The entanglement spectrum (ES) is a powerful tool for probing topological phases. While its behavior in gapped systems is well understood, its properties in gapless regimes remain unclear. In this work, we employ a quantum Monte Carlo method to study the ES of a two-dimensional square-octagon lattice Heisenberg model at quantum criticality and in the Néel phase. We find that the ES exhibits an M-shape magnon mode with a distinct sublinear dispersion, deviating from the conventional linear magnon. This behavior, similar to that of a one-dimensional long-range Heisenberg chain, reveals the emergence of relevant long-range interactions in the entanglement Hamiltonian. We demonstrate that the mechanism underlying short- and long-range interactions in the entanglement Hamiltonian can be interpreted as the confinement/deconfinement of worldlines in the path integral formulation. Our results reveal that gapless modes can fundamentally change the entanglement Hamiltonian and its spectrum, thereby offering insight into this general phenomenon. |
| title | Worldline deconfinement and emergent long-range interaction in the entanglement Hamiltonian and in the entanglement spectrum |
| topic | Strongly Correlated Electrons Statistical Mechanics |
| url | https://arxiv.org/abs/2506.10078 |