Singularities in the Loschmidt echo of quenched topological superconductors

TL;DR

This paper investigates the behavior of the Loschmidt echo in quenched topological superconductors, revealing singularities in p-wave cases and discussing theoretical modeling differences.

Contribution

It demonstrates the occurrence of singularities in the Loschmidt echo for quenched 2D p-wave topological superconductors and clarifies how mean field theory should be adapted for quantum calculations.

Findings

Loschmidt echo exhibits logarithmic singularities when quenched across topological phase transition

Singularities occur periodically in time in the p-wave superconductor case

Mean field theory needs modification to accurately compute quantum Loschmidt echo

Abstract

We study the Loschmidt echo in the quenched two-dimensional $p$-wave topological superconductor. We find that if this superconductor is quenched out of the critical point separating its topological and non-topological phases into either of the two gapful phases, its Loschmidt echo features singularities occurring periodically in time where the second derivative of the Loschmidt echo over time diverges logarithmically. Conversely, we give arguments towards $s$-wave superconductors not having singularities in their Loschmidt echo regardless of the quench. We also demonstrate that the conventional mean field theory calculates classical echo instead of its quantum counterpart, and show how it should be modified to capture the full quantum Loschmidt echo.