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

TL;DR

This paper reveals that the entanglement Hamiltonian of a gapped system can contain significant long-range interactions, leading to unexpected phase transitions that challenge previous conjectures about its local similarity to the original Hamiltonian.

Contribution

It demonstrates the presence of relevant long-range terms in the entanglement Hamiltonian of a gapped system, contradicting the Li-Haldane-Poilblanc conjecture.

Findings

Entanglement Hamiltonian exhibits long-range interactions.

Finite-temperature phase transition found in the entanglement Hamiltonian.

Results violate the Mermin-Wagner theorem, indicating long-range effects.

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.