Generation of chiral solitons in antiferromagnetic chains by a quantum quench

We analyze the time evolution of a magnetic excitation in a spin-$\frac{1}{2}$ antiferromagnetic Heisenberg chain after a quantum quench. By a proper modulation of the magnetic exchange coupling, we prepare a static soliton of total spin $\frac{1}{2}$ as an initial spin state. Using bosonization and a numerical time-dependent density matrix renormalization group algorithm, we show that the initial excitation evolves to a state composed of two counterpropagating chiral states, which interfere to yield $\langle S^z\rangle =\frac{1}{4}$ for each mode. We find that these dynamically generated states remain considerably stable as time evolution is carried out. We propose spin-Peierls materials and ultracold-atom systems as suitable experimental scenarios in which to conduct and observe this mechanism.

Figure 1

Collective excitation obtained by DMRG in a finite lattice of $N_s=99$ sites, in the absence of frustration ($\beta =0$). The soliton, represented by $\langle S_i^z\rangle$ (circles), was tuned by selecting ${\delta }_i$ in a given configuration (squares). The parameters are $\xi =1,{\delta }_0=0.3$. We also show the cumulative magnetization up to a given site (diamonds). The bosonization result for this magnitude is represented by the solid line.

Figure 2

Time evolution of $\langle S_i^z\rangle$ in the collective excitation obtained by DMRG with and without frustration for the two witness cases, (a) $\beta =0,{\delta }_0=0.3,\xi =1$ and (b) $\beta =0.24,{\delta }_0=0.3,\xi =3$. In (a), the black line corresponds to the slope in the time-space diagram of the spin velocity $v_s=\frac{\pi }{2}$ obtained by the Bethe ansatz for a homogeneous Heisenberg chain. In (b), the black line shows the spin velocity renormalized by the frustration. In both cases one observes the splitting of the soliton into two chiral modes.

Figure 3

Time evolution of the cumulative magnetization as given by DMRG (symbols) and bosonization (solid lines) in the (a) nonfrustrated and (b) frustrated ($\beta =0.24$) cases. The observed jump to $M_I=1/4$ as time evolves signals the quantum interference of left and right soliton states.

Figure 4

Time evolution of $\langle S_i^z\rangle$ for the free spin on a lattice of 41 sites at the MG point $\beta =1/2$. The solid lines correspond to the maximum group velocity according to the variational dispersion relation obtained from Ref. 6.