# Balance the units of the following hamiltonian

The following image is taken from an article and shows the hamiltonian of a spin chain model. I knew that the dimensional units in an equation must balance. To ensure this, the author took a procedure (as shown in the shaded part). With this procedure, he concluded that all parameters, J1, J2, and \lambda, have no units and hence the equation is balanced. I cannot understand this step and what is the final unit of the equation?

All three coefficinets have dimensions of energy, so $$J_2/J_1$$ and $$\lambda/J_1$$ are dimensionless.
• He just takes $J_1=1$ in whatever units he feels like. None of it affects anything. The phases of the spn chain are determined only by the ratios of the couplings. Nobody cares about the overall-energy scale in these type of models. Feb 14, 2020 at 17:43
• By "scaled to $J_1$" he means divided by $J_1$. Feb 14, 2020 at 18:10