Construction of Entangled Many-body States via the Higgs Mechanism

TL;DR

This paper introduces a novel method inspired by the Higgs mechanism to generate entangled many-body states in quantum systems without gauge structures, with potential applications in quantum simulation.

Contribution

It develops a new framework using mean-operators to create entangled states, revealing symmetry-protected topological states and diverse entangled states on various lattices.

Findings

Identified a symmetry-protected topological state with two Ising symmetries.

Constructed mean-operators that generate entanglement from trivial states.

Discussed applications to quantum simulators like Rydberg atoms and trapped ions.

Abstract

We provide a guiding principle to generate entanglement of quantum many-body states by applying key ideas of the Higgs mechanism to systems without gauge structures. Unitary operators associated with the Higgs mechanism are constructed, named as mean-operators, and employed to prepare entangled many-body states out of a trivial state. We uncover a symmetry-protectedtopological state with two Ising symmetries on a square lattice and find entangled states with different symmetries and lattices. Plausible applications to quantum simulators such as Rydberg atoms and trapped ions, are also discussed, interpreting the mean-operators as the Ising coupling gates.