Quantum Simulation of Frustrated Ising Spins with Trapped Ions
Frustration occurs when spins in the system cannot find a simple ordered spin configuration to fully satisfy all the interactions with other spins [1,2]. It can be simply illustrated by three spins with anti-ferromagnetic interactions on a triangular lattice . The situations give rise to a large ground state degeneracy, leading to magnetic analogues of liquids and ice. For quantum spins, frustrated ground states are expected to be highly related to entanglement. Recently there has been an increasing interest in simulating quantum spins with the other experimental schemes, which could eventually have exponential efficiencies over classical simulations. Here we report experimental simulations of three quantum Ising spins in textbook-type triangular geometrical frustration situation. We studied the ground state properties through adiabatic evolution from a simple polarized initial state. We observed that the degeneracy of the ground state is largest at the spin frustration case compared to all the possible nearest and next-nearest spin-spin interactions. We also observed the coherent dynamics of our evolution and proved that those highly degenerate states are entangled by using entanglement witness methods. We anticipate our demonstration is a starting point toward observing more complicated phases from frustration related to high temperature superconductors.
 H. T. Diep, Frustrated Spin Systems (World Scientific Publishing Company, 2005).
 R. Moessner and A. P. Ramirez, Phys. Today 59, 24 (Feb 2006).
 G. H. Wannier, Phys. Rev. 79, 357 (1950).