Towards ideal insulation via local Hamiltonians and near-transitionless quantum driving

When applied to band insulators, electric fields cause electronic transitions between (filled) valence bands and (empty) conduction bands. These transitions give rise to macroscopic charge transport. Berry's transitionless quantum driving concept guarantees that a certain class of auxiliary Hamiltonians can perfect the insulator by fully suppressing transitions while keeping intact the complete many-particle quantum state. If the auxiliary Hamiltonians are restricted to those achievable via local (and therefore more readily realizable) fields, one may ask: By how much can insulation still be improved? We address this question by introducing a figure of merit to characterize the impact of transitions in the presence of the auxiliary Hamiltonian. By maximizing this figure of merit, we determine the fields necessary to optimally mitigate transitions, and hence best improve the insulating character of the state, given the locality requirement. (We note that these results are encapsulated by a modified version of the localization tensor.) We illustrate these ideas via the case of the one-dimensional tight-binding model, driven by a spatially uniform electric field. Although the resulting local auxiliary Hamiltonian depends on the model, the overall strategy should improve the insulating character of any insulating state.