Hidden Frustrated Interactions and Quantum Annealing in Trapped Ion Spin-Phonon Chains

TL;DR

This paper explores how frustration effects in trapped ion chains with spin-phonon interactions lead to complex quantum phases, including spin liquids, and proposes a quantum annealing method to reach ground states.

Contribution

It reveals the role of frustration in spin-phonon coupled ion chains and introduces a mean-field quantum annealing approach for ground state preparation.

Findings

Identification of a rich quantum phase diagram with magnetic and structural orders.

Prediction of spin-liquid phases due to enhanced quantum fluctuations.

Proposal of a quantum annealing protocol for state preparation.

Abstract

We show that a trapped ion chain interacting with an optical spin-dependent force shows strong frustration effects due to the interplay between long-range interactions and the dressing by optical phases. We consider a strong spin-phonon coupling regime and predict a quantum phase diagram with different competing magnetic and structural orders. In a highly frustrated region, the system shows enhanced quantum fluctuations and entanglement characteristic of spin-liquid phases. We propose and describe within a mean-field approach a quantum annealing process to induce a quasi-adiabatic evolution towards the ground state.