Complex sentence: Instantons can then be used to describe an electron tunneling between those sectors and since these topological sectors correspond to the robustly quantized electronic phases, the instanton approximation can be used to describe the quantum Hall transitions that occur between them.
Split into simpler sentences: Instantons can then be used to describe an electron tunneling between those sectors. Since these topological sectors correspond to the robustly quantized electronic phases, the instanton approximation can be used to describe the quantum Hall transitions that occur between them.