Authors: Kenji Maeda, Joseph Whalen, Michael L. Wall, and Lincoln D. Carr

We investigate an extension of the quantum Ising model in one spatial dimension including long-range interactions.  This model describes a wide variety of two-state spin systems from heteronuclear polar molecules in optical lattices to trapped ions.  We adapt the Jordan-Wigner transformation to the long range case in a mean field approximation and thereby obtain the critical field for both ferro and antiferromagnetic phase transitions.  We then apply an extension of the infinite-domain matrix product state (iMPS) algorithm to obtain a more exact result including converged entanglement left out of our analytical approximation.  We find a 9% error between analytical and numerical results for the antiferromagnetic 1/r^3-potential.