  Counterdiabatic (CD) protocols enable fast driving of quantum states by
invoking an auxiliary adiabatic gauge potential (AGP) that suppresses
transitions to excited states throughout the driving process. Usually, the full
spectrum of the original unassisted Hamiltonian is a prerequisite for
constructing the exact AGP, which implies that CD protocols are extremely
difficult for many-body systems. Here, we apply a variational CD protocol
recently proposed by P. W. Claeys et al. [Phys. Rev. Lett. 123, 090602 (2019)]
to a two-component fermionic Hubbard model in one spatial dimension. This
protocol engages an approximated AGP expressed as a series of nested
commutators. We show that the optimal variational parameters in the
approximated AGP satisfy a set of linear equations whose coefficients are given
by the squared Frobenius norms of these commutators. We devise an exact
algorithm that escapes the formidable iterative matrix-vector multiplications
and evaluates the nested commutators and the CD Hamiltonian in analytic
representations. We then examine the CD driving of the one-dimensional Hubbard
model up to $L = 14$ sites with driving order $l \leqslant 3$. Our results
demonstrate the usefulness of the variational CD protocol to the Hubbard model
and permit a possible route towards fast ground-state preparation for many-body
systems.

Strongly Correlated Electrons;Quantum Physics