Sudden change in entanglement Hamiltonian: Phase diagram of an Ising entanglement Hamiltonian

TL;DR

This paper investigates the phase diagram of a 1D Ising entanglement Hamiltonian to understand the presence of singularities and their implications for the universality of entanglement spectrum relations.

Contribution

It clarifies the phase structure of the Ising entanglement Hamiltonian and addresses the controversy regarding the relation between entanglement and edge spectra.

Findings

Singularities can occur in the entanglement Hamiltonian.

The Li-Haldane-Poilblanc conjecture remains valid despite singularities.

The phase diagram reveals critical points affecting entanglement properties.

Abstract

The form of the entanglement Hamiltonian varies with the parameters of the original system. Whether there is a singularity is the key problem for demonstrating/negating the universality of the relation between the entanglement spectrum and edge energy spectrum. We carefully study the phase diagram of a 1D Ising entanglement Hamiltonian as an example to clarify the long-standing controversy of the general relation between the entanglement Hamiltonian and original Hamiltonian. Interestingly, even if the singularities indeed exist, the Li-Haldane-Poilblanc conjecture, i.e., the general relation between the entanglement spectrum and edge energy spectrum, seemingly still holds.