Failure to Break Clusters of Quantum Particles using Defects: Spectrum and Dynamics

We consider one-dimensional quantum models with strong interparticle interactions, which cause particles to bind together and behave as a single slow cluster. To attempt separating the particles from the clusters, we introduce defects (Zeeman splittings), but despite energy being conserved, they remain unbroken. We also investigate two-dimensional models, which provide more possibilities for spreading of particles, but find that the clusters persist. Static properties are studied via eigenvalues and eigenstates, while dynamical properties are investigated through the evolution of magnetization, participation ratio, and the probability for the clusters to survive. This study has applications in quantum computation and it can be experimentally implemented with ultracold atoms.