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We generalize the momentum average (MA) approximation to study the propertiesof models with momentum-dependent electron-phonon coupling. As in the case ofthe application of the original MA to the Holstein model, the results areanalytical, numerically trivial to evaluate, exact for both zero bandwidth andfor zero electron-phonon coupling, and are accurate everywhere in parameterspace. Comparison with available numerical data confirms this accuracy. We thenshow that further improvements can be obtained based on variationalconsiderations, using the one-dimensional breathing-mode Hamiltonian as aspecific example. For example, by using this variational MA, we obtain groundstate energies within at most 0.3% error of the numerical data.

Momentum average approximation for models with electron-phonon coupling dependent on the phonon momentum