Overlaying optical lattices for simulation of complex frustrated   antiferromagnets
  We present design techniques of special optical lattices that allow quantum simulation of spin frustration in two-dimensional systems. By carefully overlaying optical lattices with different periods and orientations, we are able to adjust the ratio between the nearest-neighbor and next-nearest-neighbor interaction strengths in a square spin lattice and realize frustration effects. We show that only laser beams of a single frequency is required, and the parameter space reachable in our design is broad enough to study the important phases in the $J_1$-$J_2$ frustrated Heisenberg model and checkerboard antiferromagnet model. By using the polarization spectroscopy for detection, distinct quantum phases and quantum phase transition points can be characterized straightforwardly. Our design thus offers a suitable setup for simulation of frustrated spin systems. 
Zhi-Xin Chen, Han Ma, Mo-Han Chen, Xiang-Fa Zhou, Lixin He, Guang-Can   Guo, Xingxiang Zhou, Yan Chen, and Zheng-Wei Zhou
cond-mat.str-el quant-ph