Abstract
Equilibrium topological phases are robust against weak static disorder but may break down in the strong disorder regime. Here we explore the stability of the quench-induced emergent dynamical topology in the presence of dynamical noise. We develop an analytic theory and show that for weak noise, the quantum dynamics induced by quenching an initial trivial phase to Chern insulating regime exhibits robust emergent topology on certain momentum subspaces called band inversion surfaces (BISs). The dynamical topology is protected by the minimal oscillation frequency over the BISs, mimicking a bulk gap of the dynamical phase. Singularities emerge in the quench dynamics, with the minimal oscillation frequency vanishing on the BISs if increasing noise to critical strength, manifesting a dynamical topological transition, beyond which the emergent topology breaks down. Two types of dynamical transitions are predicted. Interestingly, we predict a sweet spot in the critical transition when noise couples to all three spin components in the same strength, in which case the dynamical topology survives at arbitrarily strong noise regime. This work unveils novel features of the dynamical topology under dynamical noise, which can be probed with control in experiment.
Highlights
The topological quantum phases [1,2,3,4,5,6] are defined on the ground state of a system in equilibrium with a nontrivial bulk topological invariant, and host topologically protected gapless boundary modes through the celebrated bulk-boundary correspondence [5,6]
In the weak-noise regime, we show that the dynamical topology emerging on the dynamical band-inversion surfaces is protected by the minimal oscillation frequency which mimics the bulk gap of the emergent dynamical phase
We have investigated the effects of dynamical noise on the quench-induced emergent dynamical topology, with universal results being predicted
Summary
The topological quantum phases [1,2,3,4,5,6] are defined on the ground state of a system in equilibrium with a nontrivial bulk topological invariant, and host topologically protected gapless boundary modes through the celebrated bulk-boundary correspondence [5,6]. Topological patterns are predicted to emerge on the (d − 1)D momentum subspaces called band-inversion surfaces (BISs) in quantum dynamics, which universally correspond to the bulk topology of the dD equilibrium topological phase [42,43,44,45,46,47,48]. This dynamical bulk-surface correspondence provides new schemes to characterize and detect the equilibrium topological phase via nonequilibrium quench dynamics, and has been generalized to various topological systems [49,50,51,52,53], with the experimental verifications having been widely reported recently [54,55,56,57,58,59,60].
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