  We present a microscopic theory for quantum thermoelectric and heat transport
in the Schwarzian regime of the Sachdev-Ye-Kitaev (SYK) model. As a charged
fermion realization of the SYK model in nanostructures we assume a setup based
on a quantum dot connected to the charge reservoirs through weak tunnel
barriers. We analyze particle-hole symmetry breaking effects crucial for both
Seebeck and Peltier coefficients. We show that the quantum charge and heat
transport at low temperatures are defined by the interplay between elastic and
inelastic processes such that the inelastic processes provide a leading
contribution to the transport coefficients at the temperatures that are smaller
compared to the charging energy. We demonstrate that both electric and thermal
conductance obey a power law in temperature behavior, while thermoelectric,
Seebeck, and Peltier coefficients are exponentially suppressed. This represents
selective suppression of only nondiagonal transport coefficients. We discuss
the validity of the Kelvin formula in the presence of a strong Coulomb
blockade.
