Signatures of the Kondo effect in the electrical conductance of strongly correlated quantum dots are well understood both experimentally and theoretically, while those in the thermopower have been the subject of recent interest. Here, we extend theoretical work [T. A. Costi, Phys. Rev. B {bf 100}, 161106(R) (2019)] on the field-dependent thermopower of such systems, and carry out calculations in order to address a recent experiment on the field dependent thermoelectric response of Kondo-correlated quantum dots [A. Svilans {em et al.,} Phys. Rev. Lett. {bf 121}, 206801 (2018)]. In addition to the sign changes in the thermopower at temperatures $T_1(B)$ and $T_2(B)$ (present also for $B=0$) in the Kondo regime, an additional sign change was found [T. A. Costi, Phys. Rev. B {bf 100}, 161106(R) (2019)] at a temperature $T_0(B)<T_1(B)<T_2(B)$ for fields exceeding a gate-voltage dependent value $B_0$, where $B_0$ is comparable to, but larger, than the field $B_c$ at which the Kondo resonance splits. We describe the evolution of the Kondo-induced sign changes in the thermopower at temperatures $T_0(B),T_1(B)$ and $T_2(B)$ with magnetic field and gate voltage from the Kondo regime to the mixed valence and empty orbital regimes. By carrying out detailed NRG calculations for the above quantities we address the recent experiment by A. Svilans {em et al.,} Phys. Rev. Lett. {bf 121}, 206801 (2018), which measures the field-dependent thermoelectric response of InAs quantum dots exhibiting the Kondo effect, finding good agreement for the overall trends in the measured field- and temperature-dependent thermoelectric response as a function of gate voltage.
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