Interaction-Induced Bloch Geometry and Transverse Thermoelectric Transport

Electron–electron interactions can reconstruct Bloch wave functions, changing their geometry and the associated thermoelectric response. We derive the linear thermoelectric response within the Hartree–Fock (HF) approximation using the thermal length-gauge density-matrix approach, resolving Drude, symmetric quantum-metric, and antisymmetric Berry-curvature contributions. In a noninteracting Bloch eigenbasis, we separate the reconstructed Berry connection into the noninteracting connection and an interaction connection. This gives bare, coherence, and interaction-connection contributions to the anomalous thermoelectric response. We determine the constraints imposed by spatial inversion, rotational, time-reversal, and combined symmetries on the three transport channels. In the relaxation-time approximation, the leading weak-broadening behavior is ${\mathrm{\Gamma }}^{-1}$ for the Drude contribution, $\mathrm{\Gamma }$ for the quantum-metric contribution, and ${\mathrm{\Gamma }}^0$ for the Berry-curvature contribution. The interband scalings apply away from band degeneracies. Self-consistent calculations for the triangular-lattice extended Hubbard model illustrate how interactions generate Berry curvature and a quantum metric, change the symmetry of the system, and thereby contribute to transverse thermoelectric transport.