Many-body interactions with single-electron quantum dots for topological quantum computation

摘要

We show that a many-body system of single-electron quantum dots, whose orbital states are dressed by a globalmagnetic field, can be described by an effective Hamiltonian with an anisotropic XZ spin-spin interaction whichis proportional to the Zeeman splitting. We show that these interaction potentials give rise to spin-dependentHubbard models with tunable nearest neighbor two-body and three-body interactions. The two-body interactionscan even be switched off via the external electric field, and hence the three-body interaction plays a dominant role.The derivation of these effective interaction potentials follows from a well-controlled and systematic expansioninto many-body interaction terms. Models of this type have appeared in the recent discussion of exotic quantumphases, in particular in the context of topological quantum phases and quantum computing, and we show thatquantum dots can be regarded as a realistic experimental route which provides the basic building blocks andtechniques toward the study of these phenomena. The main application of this derived model is to developtopological quantum computation.