Topological order following a quantum quench

We determine the conditions under which topological order survives a rapid quantum quench. Specifically, we consider the case where a quantum spin system is prepared in the ground state of the toric code model and, after the quench, it evolves with a Hamiltonian that does not support topological order. We provide analytical results supported by numerical evidence for a variety of quench Hamiltonians. The robustness of topological order under nonequilibrium situations is tested by studying the topological entropy and a dynamical measure, which makes use of the similarity between partial density matrices obtained from different topological sectors.

Figure 1

(Color online) Numerical results for the quench $H_3$ with couplings $J_1/J_2=0.33$. (a) Absolute overlap $\left|⟨{\Psi }_0|\Psi \left(t\right)⟩\right|$ on lattices with $N=8,12$ spins. (b) $S_{\text{topo}}\left(t\right)$ for the $N=8,12$ lattices and fidelity $\mathcal{F}\left(t\right)$ for the $N=12$ lattice.

Figure 2

(Color online) Numerical results for the quench $H_4$ with $h=0.34$. (a) Absolute overlap $\left|⟨{\Psi }_0|\Psi \left(t\right)⟩\right|$ on lattices with $N=8,12,18$ spins. (b) $S_{\text{topo}}\left(t\right)$ for the $N=8,12,18$ lattices and fidelity $\mathcal{F}\left(t\right)$ for the $N=18$ lattice.

Figure 3

(Color online) Numerical results for the quench $H_5$. (a) $\left|⟨{\Psi }_0|\Psi \left(t\right)⟩\right|$ on the $N=8,12$ lattices for $J_1=J_2=0.033$. (b) $S_{\text{topo}}\left(t\right)$ for the $N=8,12$ lattices and $\mathcal{F}\left(t\right)$ for the $N=12$ lattice for $J_1=J_2=0.033$. (c) The same as in (a) but for $J_1=J_2=3.3$. (d) The same as in (b) but for $J_1=J_2=3.3$.