Numerical investigations of the extensive entanglement Hamiltonian in quantum spin ladders

TL;DR

This paper numerically investigates the properties of extensive entanglement in coupled quantum spin chains, revealing universal behaviors and symmetry-breaking phenomena, and providing a foundation for future research in quantum many-body entanglement.

Contribution

It provides a comprehensive numerical analysis of extensive entanglement in quantum spin ladders, highlighting universal behaviors and the role of conformal field theory.

Findings

Identification of gapless and symmetry-breaking entanglement Hamiltonians

Application of conformal field theory to characterize universal behavior

Establishment of a framework for exploring extensive entanglement in quantum systems

Abstract

Entanglement constitutes one of the key concepts in quantum mechanics and serves as an indispensable tool in the understanding of quantum many-body systems. In this work, we perform extensive numerical investigations of extensive entanglement properties of coupled quantum spin chains. This setup has proven useful for e.g. extending the Lieb-Schultz-Mattis theorem to open systems, and contrasts the majority of previous research where the entanglement cut has one lower dimension than the system. We focus on the cases where the entanglement Hamiltonian is either gapless or exhibits spontaneous symmetry breaking behavior. We further employ conformal field theoretical formulae to identify the universal behavior in the former case. The results in our work can serve as a paradigmatic starting point for more systematic exploration of the largely uncharted physics of extensive entanglement, both analytical and numerical.