Quantum simulating the frustrated Heisenberg model in a molecular dipolar crystal

•We simulate spin models with polar molecules in a dipolar crystal.•We employ a master equation to describe the dynamics of the system.•The influence of the lattice vibrations is calculated.

We study the simulation of spin models with polar molecules in a dipolar crystal. We employ a master equation approach to describe the dynamics of the system and to research the dissipation of the model. The reduced dynamics of the polar molecules lead to frustrated Heisenberg models with tuneable long-range interactions, via spin-dependent dipole–dipole interactions forces to the lattice vibrations. The influence of the lattice vibrations is calculated and analyzed in detail.