Thermoelectric properties and Wiedemann-Franz-like relations in mixed-dimensional QEDs from particle-vortex dualities

We consider the thermoelectric properties of the mixed-dimensional quantum electrodynamics of the relativistic Dirac fermion and Wilson-Fisher boson. These models are self-dual, and can form nontrivial many-body phases depending on the values of chemical potential, background magnetic field and the electromagnetic fine-structure constant. Using particle-vortex duality, we derive a variety of thermoelectric relations for strongly interacting phases with classic paradigms such as the Wiedemann-Franz law and the Mott's relation in the dual weakly interacting regimes. Besides, at the self-dual point, for the fermionic theory we find the ratio of thermal conductivity of electrical conductivity depends on the determinant of the Seebeck tensor and the phenomenological parameter Hall angle theta(H). As for the bosonic theory, the dual fermion description explains how its Seebeck tensor varies depending on the dynamic regime characterized by theta(H).

Automated summary

The study investigates the thermoelectric properties of mixed-dimensional quantum electrodynamics of relativistic Dirac fermions and Wilson-Fisher bosons, revealing their self-dual nature and ability to form nontrivial many-body phases under different parameter values. Using particle-vortex duality, a variety of thermoelectric relations for strongly interacting phases were derived, showing dependencies on the Seebeck tensor determinant and the Hall angle theta(H), among other parameters, at the self-dual point. The dual fermion description sheds light on how the Seebeck tensor of the bosonic theory varies according to the dynamic regime characterized by theta(H).