Dynamical frustration in ANNNI model and annealing

TL;DR

This paper investigates the limitations of classical and quantum annealing methods in reaching the ground state of the ANNNI model, especially near the fully frustrated point where residual energy decays very slowly.

Contribution

It demonstrates the failure of annealing techniques to efficiently find ground states in the ANNNI model at high frustration levels, highlighting the challenge near the fully frustrated point.

Findings

Classical annealing works well for low frustration.

Quantum annealing is ineffective near the fully frustrated point.

Residual energy decays slowly at the fully frustrated point.

Abstract

Zero temperature quench in the Axial Next Nearest Neighbour Ising (ANNNI) model fails to bring it to its ground state for a certain range of values of the frustration parameter $\kappa$, the ratio of the next nearest neighbour antiferromagnetic interaction strength to the nearest neighbour one. We apply several annealing methods, both classical and quantum, and observe that the behaviour of the residual energy and the order parameter depends on the value of $\kappa$ strongly. Classical or thermal annealing is found to be adequate for small values of $\kappa$. However, neither classical nor quantum annealing is effective at values of $\kappa$ close to the fully frustrated point $\kappa=0.5$, where the residual energy shows a very slow algebraic decay with the number of MCS.