Variational principle of the zig-zag optical lattice model in quantum physics

The zig-zag optical lattice model, which plays a major role in quantum physics, is considered in this research. With the aid of the semi-inverse method (SIM), the variational principle (VP) is developed via introducing the trial-Lagrange function (TLF). The detailed derivation process is given and the correctness of the established VP is verified with the Euler–Lagrange equations that were found via computing the stationary conditions. As far as the authors know, the VP is first probed and explored via the SIM in this study. The VP can unfold the intrinsic connections of the different physical quantities, help us better understand the essence of physical phenomena and provide new insights into the exploration and application of the variational approach.