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arXiv:1209.3898 · Physical Review B

Entanglement, fractional magnetization, and long-range interactions

Andrea Cadarso, Mikel Sanz, Michael M. Wolf, J. I. Cirac, David Pérez-Garcı́a

Published Jan 11, 2013• 24 citations
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Abstract

Based on the theory of matrix product states, we give precise statements and complete analytical proofs of the following claim: A large fractionalization in the magnetization or the need of long-range interactions imply large entanglement in the state of a quantum spin chain.
DOI
10.1103/physrevb.87.035114

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Quantum spin chains arise naturally from perturbative large- N field theories and matrix models. The Hamiltonian of such a model is a long-range deformation of nearest-neighbour type interactions. Here, we study the most general long-range integrable spin chain with spins transforming in the fundamental representation of . We derive the Hamiltonian and the corresponding asymptotic Bethe ansatz at the leading four perturbative orders with several free parameters. Furthermore, we propose Bethe equations for all orders and identify the moduli of the integrable system. We finally apply our results to plane-wave matrix theory and show that the Hamiltonian in a closed sector is not of this form and therefore not integrable beyond the first perturbative order. This also implies that the complete model is not integrable.
We introduce a class of spin models with long-range interactions—in the sense that they extend significantly beyond their nearest neighbors—whose ground states can be constructed analytically and that have a simple matrix product state representation. This enables the detailed study of ground state properties, such as correlation functions and entanglement, in the thermodynamic limit. The spin models presented here are closely related to lattice gases of strongly interacting polar molecules, or Rydberg atoms that feature an excluded volume or blockade interaction. While entanglement is only present between spins that are separated by no more than a blockade length, we show that non-classical correlations can extend much further, and we analyze them through quantum discord. We furthermore identify a set of seemingly critical points where the ground state approaches a crystalline state with a filling fraction that is given by the inverse of the blockade length. We analyze the scaling properties in the vicinity of this parameter region and show that the correlation length possesses a non-trivial dependence on the blockade length.