Simulating An Exact One-Dimensional Transverse Ising Model In An Optical Lattice

A spinless Bose-Hubbard model in a one-dimensional (1D) double-chain tilted lattice is numerically studied at unit filling per cell. When each atom is localized in a two-site cell, the low-energy effective model gives rise to an exact textbook model of the 1D transverse Ising model via superexchange interaction. To validate the effective transverse Ising model, we calculate the energy spectrum and the nearest-neighbor correlation functions of the states in a subspace of the Bose-Hubbard model which is equivalent to the Hilbert space of a spin-1/2 magnetic model. The results show good consistency with the effective transverse Ising model, and we show that it is possible to simulate the dynamical quantum phase transition of the 1D transverse Ising model exactly with such a double-chain Bose-Hubbard model. Our results may provide some inspirations for realizing and exploring an exact 1D transverse Ising model in ultracold neutral atom systems.