Dynamical Quantum Phase Transitions: A Geometric Picture

Johannes Lang, Bernhard Frank, Jad C. Halimeh

Published 2018-04-24Version 1

The Loschmidt echo (LE) is a purely quantum-mechanical quantity, as such its determination for large quantum many-body systems requires an exceptionally precise knowledge of all eigenstates and eigenenergies. One might therefore be tempted to dismiss the applicability of any approximations to the underlying time evolution as hopeless. However, using the fully connected transverse-field Ising model (FC-TFIM) as an example, we show that this indeed is not the case, and that a simple semiclassical approximation to systems well described by mean-field theory (MFT) is in fact in good quantitative agreement with the exact quantum-mechanical calculation. Beyond the potential to capture the entire phase diagram of these models, the method presented here also allows for an intuitive geometric interpretation of the fidelity return rate at any temperature, thereby connecting the order parameter dynamics and the Loschmidt echo in a common framework.