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By combining the Baeriswyl wavefunction with equilibrium and time-dependentvariational principles, we develop a non-equilibrium formalism to study quantumquenches for two dimensional spinless fermions with nearest-neighbour hoppingand repulsion. The variational ground state energy and the short time dynamicsagree convincingly with the results of numerically exact simulations. We findthat depending on the initial and final interaction strength, the quenchedsystem either exhibits undamped oscillations or relaxes to a time independentsteady state. The time averaged expectation value of the CDW order parameterrises sharply when crossing from the steady state regime to the oscillatingregime, indicating that the system, being non-integrable, shows signs ofthermalization with an effective temperature above or below the equilibriumcritical temperature, respectively.

Quantum quench in 2D using the variational Baeriswyl wavefunction