We propose a scheme to simulate one-dimensional $\mathit{XXZ}$-type Heisenberg spin models with competing interactions between nearest neighbors (NNs) and next NNs in photon-coupled microcavities. Our scheme 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 a powerful capability allows us to simulate frustration phenomena and disorder behaviors in one-dimensional 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.

• Received 29 September 2009

DOI:https://doi.org/10.1103/PhysRevA.81.022303