Time Reversal Polarization and a Z 2 Adiabatic Spin Pump

摘要: We introduce and analyze a class of one-dimensional insulating Hamiltonians that, when adiabatically varied in an appropriate closed cycle, define ``${Z}_{2}$ pump.'' For isolated system, single cycle the pump changes expectation value spin at each end even spin-orbit interactions violate conservation spin. A second however, returns system to its original state. When coupled leads, we show that ${Z}_{2}$ functions as sense define, transmits finite, though nonquantized, cycle. is characterized by topological invariant analogous Chern characterizes charge pump. The closely related quantum Hall effect, which invariant. This work presents alternative formulation clarifies both physical mathematical meaning crucial role played time reversal symmetry, concept polarization, signals presence or absence Kramers degenerate states. noninteracting electrons, derive formula for polarization Berry's phase polarization. interacting Abelian bosonization provides simple discuss implications argue particular classification effect valid electron interactions.