  The electrical Hall conductivities of any anisotropic interacting system with
reflection symmetry obey sigma_{xy} = - sigma_{yx}. In contrast, we show that
the analogous relation between the transverse thermoelectric Peltier
coefficients, alpha_{xy}= - alpha_{yx}, does not generally hold in the same
system. This fact may be traced to interaction contributions to the heat
current operator and the mixed nature of the thermoelectric response functions.
Remarkably, however, it appears that emergence of quasiparticles at low
temperatures forces alpha_{xy} = - alpha_{yx}. This suggests that
quasiparticle-free groundstates (so-called non-Fermi liquids) may be detected
by examining the relationship between alpha_{xy} and alpha_{yx} in the presence
of reflection symmetry and microscopic anisotropy. These conclusions are based
on the following results: (i) The relation between the Peltier coefficients is
exact for elastically scattered noninteracting particles; (ii) It holds
approximately within Boltzmann theory for interacting particles when elastic
scattering dominates over inelastic processes. In a disordered Fermi liquid the
latter lead to deviations that vanish as T^3. (iii) We calculate the
thermoelectric response in a model of weakly-coupled spin-gapped Luttinger
liquids and obtain strong breakdown of antisymmetry between the off-diagonal
components of alpha. We also find that the Nernst signal in this model is
enhanced by interactions and can change sign as function of magnetic field and
temperature.

Strongly Correlated Electrons;Superconductivity