Quantum quenches in an interacting field theory: Full quantum evolution versus semiclassical approximations

We develop a truncated Hamiltonian method to investigate the dynamics of the (1 +1 ) -dimensional ϕ⁴ theory following quantum quenches. The results are compared to two different semiclassical approaches, the self-consistent Gaussian approximation and the truncated Wigner approximation, and used to determine the range of validity of these widely used approaches. We show that the self-consistent approximation is strongly limited in comparison to the truncated Hamiltonian method which for larger cutoffs is practically exact for the parameter range studied. We find that the self-consistent approximation is only valid when the effective mass is in the vicinity of the renormalized mass. Similarly to the self-consistent approximation, the truncated Wigner approximation (TWA) is not able to capture the correct mass renormalization, and breaks down for strong enough interactions where the bare mass becomes negative. We attribute the failure of TWA to the presence of a classical symmetry-broken fixed point. Aside from establishing the truncated Hamiltonian approach as a powerful tool for studying the dynamics of the ϕ⁴ model, our results on the limitation of semiclassical approximations are expected to be relevant for modeling the dynamics of other quantum field theories.