Singularities in the Loschmidt echo of quenched topological superconductors

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.

References in corpus (13)

• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Dynamical Quantum Phase Transitions in the Transverse Field Ising Model
• Direct observation of dynamical quantum phase transitions in an interacting many-body system
• Resonantly-paired fermionic superfluids
• Observation of a dynamical topological phase transition
• Quantum phase transitions across p-wave Feshbach resonance
• Topological classification of dynamical phase transitions
• First order dynamical phase transitions
• Mixed state dynamical quantum phase transition and emergent topology
• Quantum quench in a p + i p superfluid: Winding numbers and topological states far from equilibrium
• Faster than Lyapunov decays of classical Loshcmidt echo
• Wigner negativity in spin-$j$ systems
• Loschmidt Echo of Far-From-Equilibrium Fermionic Superfluids