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We investigate the pumped charge and spin at zero-bias by adiabaticmodulation of two control parameters using the full counting statistics withquantum master equation approach. First we study higher order effects of thepumping frequency in general Markov systems and show the equivalence betweenour approach and the real-time diagrammatic approach. An adiabatic modulationof the control parameters induces the Berry-Sinitsyn-Nemenman (BSN) phase. Weshow that the origin of the BSN phase is a non-adiabatic effect. Theadiabatically pumped charge (spin) is given by a summation of (i) a timeintegral of the instantaneous steady charge (spin) current and (ii) a geometricsurface integral of the BSN curvature, which results from the BSN phase. Inquantum dots (QDs) weakly coupled to two leads, we show that (i) is usuallydominant if the thermodynamic parameters are modulated although it is zero ifthe thermodynamic parameters are fixed to zero-bias. To observe the spineffects, we consider collinear magnetic fields, which relate to spins throughthe Zeeman effect, with different amplitudes applying to the QDs and the leads.For interacting one level QD, we calculate analytically the pumped charge andspin by modulating the magnetic fields and the coupling strengths to the leadsin the weak and strong interacting limits. We show that the difference betweenthese two limits appears through the averages of the numbers of the electronwith up and down spin in the QD. For the quantum pump by the modulation of themagnetic fields of the QD and one lead, the energy-dependences of linewidthfunctions, which are usually neglected, are essential.

Interaction effect on adiabatic pump of charge and spin in quantum dot