Adiabatic tracking of quantum many-body dynamics

The nonadiabatic dynamics of a many-body system driven through a quantum critical point can be controlled using counterdiabatic driving, where the formation of excitations is suppressed by assisting the dynamics with auxiliary multiple-body nonlocal interactions. We propose an alternative scheme which circumvents practical challenges to realize shortcuts to adiabaticity in mesoscopic systems by tailoring the functional form of the auxiliary counterdiabatic interactions. A driving scheme resorting in short-range few-body interactions is shown to generate an effectively adiabatic dynamics.

Figure 1

(a) Schematic of the variational construction of the ansatz of the form Eq. (3) to the “exact” auxiliary CD term in Eq. (1) for possible experimental implementation in a trapped ion chain. ${\tilde{\mathcal{H}}}_{\mathrm{aux}}^{[\mathfrak{K},\mathcal{R}]}$ corresponds to the action of an itinerant “train” of $\mathfrak{K}$-partite Pauli interactions between all possible permutations of a $\mathfrak{K}$-tuple of spins within the range $\mathcal{R}$ and with optimal amplitudes $h_{i_1,...,i_{\mathfrak{K}}}^{{\alpha }_1,...,{\alpha }_{\mathfrak{K}}}$ obtained from the contraction pattern depicted in (b).

Figure 2

(a) Suppression of DOE following the passage through the QCP induced by the variational ansatz restricted to two-body interactions, as in (10), as a function of the quench rate $v$ in a linear quantum Ising chain for different system sizes. At fast quench rates, the efficiency of the ansatz in suppressing excitations saturates and a further suppression can be achieved by including higher-order multiple-body terms, as (b) depicts.

Figure 3

(a) Time evolution of the state preparation infidelity during a shortcut to the adiabatic driving of the ground state of a quantum Ising chain. The fidelity can be improved significantly by incorporating higher-body interactions at a truncated range of $\tilde{\mathcal{R}}={\mathcal{R}}_{max}-4$. (b) Real-time flow of the interaction amplitudes associated with the implementation of the full-range two-body ansatz as in Eq. (10) during passage through QCP of the model denoted by $s_c$. The color maps in the insets visualize the strength of two-body interactions $h_{i_1,i_2}^{y,z}$ among all pairs of spins at sites $(i_1,i_2)$ in the chain.