Quantum simulation of Heisenberg spin chains with next nearest neighbor   interactions in coupled cavities
  We propose a scheme to simulate one-dimensional XXZ-type Heisenberg spin models with competing interactions between nearest-neighbors (NNs) and next-NNs in photon-coupled micro-cavities. Our scheme, for the first time, exploits the rich resources and flexible controls available in such a system to realize arbitrarily adjustable ratios between the effective NN and next-NN coupling strengths. Such powerful capability allows us to simulate frustration phenomena and disorder behaviors in 1-d systems arising from next-NN interactions, a large class of problems of great importance in condensed matter physics. Our scheme is robust due to the lack of atomic excitations which suppresses spontaneous emission and cavity decay strongly. 
Zhi-Xin Chen, Zheng-Wei Zhou, Xingxiang Zhou, Xiang-Fa Zhou, and   Guang-Can Guo
quant-ph