We present a formulation for investigating quench dynamics across
quantum phase transitions in the presence of decoherence. We formulate
decoherent dynamics induced by continuous quantum non-demolition
measurements of the instantaneous Hamiltonian. We generalize the
well-studied universal Kibble-Zurek behavior for linear temporal drive
across the critical point. We identify a strong decoherence regime
wherein the decoherence time is shorter than the standard correlation
time, which varies as the inverse gap above the groundstate. In this
regime, we find that the freeze-out time
\bar{t}\sim\tau^{{2\nu z}/({1+2\nu z})}t-∼τ2νz/(1+2νz)
for when the system falls out of equilibrium and the associated
freeze-out length \bar{\xi}\sim\tau^{\nu/({1+2\nu z})}ξ‾∼τν/(1+2νz)
show power-law scaling with respect to the quench rate
1/\tau1/τ,
where the exponents depend on the correlation length exponent
\nuν
and the dynamical exponent zz
associated with the transition. The universal exponents differ from
those of standard Kibble-Zurek scaling. We explicitly demonstrate this
scaling behavior in the instance of a topological transition in a Chern
insulator system. We show that the freeze-out time scale can be probed
from the relaxation of the Hall conductivity. Furthermore, on
introducing disorder to break translational invariance, we demonstrate
how quenching results in regions of imbalanced excitation density
characterized by an emergent length scale which also shows universal
scaling. We perform numerical simulations to confirm our analytical
predictions and corroborate the scaling arguments that we postulate as
universal to a host of systems.
Probing non-Hermitian phase transitions in curved space via quench dynamics
