Non-classical correlations in a class of spin chains with long-range interactions and exactly solvable ground states

Abstract

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.

Keywords

• spin systems
• long-range interactions
• quantum correlations