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arXiv · 2309.16089

Relevant long-range interaction of the entanglement Hamiltonian emerges from a short-range gapped system

Chuhao Li·Rui-Zhen Huang·Yi-Ming Ding·Zi Yang Meng·Yan-Cheng Wang·Zheng Yan
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Abstract

Beyond the Li-Haldane-Poilblanc conjecture, we find the entanglement Hamiltonian (EH) is actually not closely similar to the original Hamiltonian on the virtual edge. Unexpectedly, the EH has some relevant long-range interacting terms which hugely affect the physics. Without loss of generality, we study a spin-1/2 Heisenberg bilayer to obtain the entanglement information between the two layers through our newly developed quantum Monte Carlo scheme, which can simulate large-scale EH. Although the entanglement spectrum carrying the Goldstone mode seems like a Heisenberg model on a single layer, which is consistent with Li-Haldane-Poilblanc conjecture, we demonstrate that there actually exists a finite-temperature phase transition of the EH. The results violate the Mermin-Wagner theorem, which means there should be relevant long-range terms in the EH. It reveals that the Li-Haldane-Poilblanc conjecture ignores necessary corrections for the EH which may lead totally different physics.

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Chuhao Li, Rui-Zhen Huang, Yi-Ming Ding, Zi Yang Meng, Yan-Cheng Wang, Zheng Yan. 2023-09-28. Relevant long-range interaction of the entanglement Hamiltonian emerges from a short-range gapped system. https://doi.org/10.1103/physrevb.109.195169

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