Entanglement Spectroscopy and probing the Li-Haldane Conjecture in Topological Quantum Matter

TL;DR

This paper proposes using synthetic quantum systems to measure entanglement spectra and explore the Li-Haldane conjecture, aiming to experimentally identify topological order in complex quantum systems.

Contribution

It introduces a method to experimentally probe the entanglement-edge state relationship using the Entanglement Hamiltonian in current quantum technologies.

Findings

Feasibility demonstrated for quantum Hall states on 2D lattices.

Feasibility demonstrated for symmetry protected topological states in 1D.

Provides a pathway for experimental detection of topological order.

Abstract

Topological phases are characterized by their entanglement properties, which is manifest in a direct relation between entanglement spectra and edge states discovered by Li and Haldane. We propose to leverage the power of synthetic quantum systems for measuring entanglement via the Entanglement Hamiltonian to probe this relationship experimentally. This is made possible by exploiting the quasi-local structure of Entanglement Hamiltonians. The feasibility of this proposal is illustrated for two paradigmatic examples realizable with current technology, an integer quantum Hall state of non-interacting fermions on a 2D lattice and a symmetry protected topological state of interacting fermions on a 1D chain. Our results pave the road towards an experimental identification of topological order in strongly correlated quantum many-body systems.