Performance evaluation of the discrete truncated Wigner approximation for quench dynamics of quantum spin systems with long-range interactions

The discrete truncated Wigner approximation (DTWA) is a powerful tool for analyzing dynamics of quantum-spin systems. Since the DTWA includes the leading order quantum corrections to a mean-field approximation, it is naturally expected that the DTWA becomes more accurate when the range of interactions of the system increases. However, quantitative corroboration of this expectation is still lacking mainly because it is generally difficult in a large system to evaluate a timescale on which the DTWA is quantitatively valid. In order to investigate how the validity timescale depends on the interaction range, we analyze dynamics of quantum spin models subjected to a sudden quench of a magnetic field by means of both DTWA and its extension including the second-order correction, which is derived from the Bogoliubov-Born-Green-Kirkwood-Yvon equation. We also develop a new formulation for calculating the second-order Renyi entropy within the framework of the DTWA. By comparing the time evolution of the Renyi entropy computed by the DTWA with that by the extension including the correction, we find that both in the one- and two-dimensional systems the validity timescale increases algebraically with the interaction range.