# Transverse Thermoelectric Response of an Interacting Quasi-One-Dimensional Electronic System in a Magnetic Field

## Dror Orgad

We show that contrary to the electrical Hall conductivity, the transverse thermoelectric linear response of an interacting system with reflection symmetry does not generally obey \alpha_{xy} = – \alpha_{yx}. Such a relation does hold in the free case and its violation is therefore a clear sign of interactions. We demonstrate this point by calculating the transverse thermoelectric transport coefficients in a system of weakly coupled Luttinger liquids subject to a magnetic field. Both off-diagonal elements of the Peltier tensor contain an antisymmetric piece, which is proportional to the magnetization density of the system. However, the transport coefficient relating the electrical current between chains to the temperature gradient along the chains acquires an additional contribution that breaks the antisymmetry. In the presence of a spin gap it causes the coefficient, and hence also the Nernst signal, to change sign as function of magnetic field and temperature.