The Folded Spin-1/2 XXZ Model: I. Diagonalisation, Jamming, and Ground State Properties

Abstract

We study an effective Hamiltonian generating time evolution of states on intermediate time scales in the strong-coupling limit of the spin-1/2 XXZ model. To leading order, it describes an integrable model with local interactions. We solve it completely by means of a coordinate Bethe Ansatz that manifestly breaks the translational symmetry. We demonstrate the existence of exponentially many jammed states and estimate their stability under the leading correction to the effective Hamiltonian. Some ground state properties of the model are discussed.

47 pages, 6 figures

References in corpus (3)

• Many body localization and thermalization in quantum statistical mechanics
• Experimental Observation of a Generalized Gibbs Ensemble
• Emergent Fermions and Anyons in the Kitaev Model

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