Characterizing Topological Excitations of a Long-Range Heisenberg Model with Trapped Ions

TL;DR

This paper proposes a Floquet protocol to realize a long-range Heisenberg model in trapped ions, characterizing its topological excitations and phase transitions through analytical, numerical, and interferometric methods.

Contribution

It introduces a novel Floquet scheme for simulating a long-range Heisenberg model and presents methods to detect topological excitations and phase transitions.

Findings

Identified a quantum phase transition from a liquid to a valence bond solid.

Demonstrated measurement protocols for topological invariants.

Proposed interferometric techniques to characterize topological excitations.

Abstract

Realizing and characterizing interacting topological phases in synthetic quantum systems is a formidable challenge. Here, we propose a Floquet protocol to realize the antiferromagnetic Heisenberg model with power-law decaying interactions. Based on analytical and numerical arguments, we show that this model features a quantum phase transition from a liquid to a valence bond solid that spontaneously breaks lattice translational symmetry and is reminiscent of the Majumdar-Ghosh state. The different phases can be probed dynamically by measuring the evolution of a fully dimerized state. We moreover introduce an interferometric protocol to characterize the topological excitations and the bulk topological invariants of the interacting many-body system.