Quantum quenches in an interacting field theory: full quantum evolution vs. semi-classical approximations

TL;DR

This paper develops a truncated Hamiltonian method to accurately study quantum quenches in the (1+1)d φ^4 theory and compares it with semi-classical approximations, revealing their limitations and validity range.

Contribution

The paper introduces a truncated Hamiltonian approach for (1+1)d φ^4 theory dynamics and assesses semi-classical methods, establishing the former as a highly accurate tool.

Findings

Truncated Hamiltonian method is nearly exact for studied parameters.

Self-consistent approximation is limited near the renormalized mass.

Truncated Wigner approximation fails for strong interactions due to symmetry breaking.

Abstract

We develop a truncated Hamiltonian method to investigate the dynamics of the $(1+1)d~\phi^4$ theory following quantum quenches. The results are compared to two different semi-classical 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 renormalised mass. Similarly to the self-consistent approximation, the truncated Wigner approximation is not able to capture the correct mass renormalisation, 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. Besides establishing the truncated Hamiltonian approach as a powerful tool for studying the dynamics of the $\phi^4$ model, our results on the limitation of semi-classical approximations are expected to be relevant for modelling the dynamics of other quantum field theories.