Worldline deconfinement and emergent long-range interaction in the entanglement Hamiltonian and in the entanglement spectrum

TL;DR

This study uses quantum Monte Carlo to analyze the entanglement spectrum of a 2D Heisenberg model at criticality, revealing long-range interactions and deconfinement phenomena affecting gapless modes.

Contribution

It uncovers the emergence of long-range interactions in the entanglement Hamiltonian at quantum criticality, linked to worldline confinement/deconfinement mechanisms.

Findings

Entanglement spectrum shows an M-shape magnon mode with sublinear dispersion.

Long-range interactions in the entanglement Hamiltonian resemble those in a 1D long-range Heisenberg chain.

Gapless modes can fundamentally alter the entanglement Hamiltonian and spectrum.

Abstract

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 N\'eel 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.