Hall Angle of a Spatially Random Vector Model

TL;DR

This paper investigates the Hall angle and resistivity in a spatially random vector model relevant to strange metals, finding linear resistivity persists but Hall angle signatures differ from experimental observations.

Contribution

It extends the SYK-like spatially random coupling model to include magnetic fields and analyzes the resulting transport properties, highlighting the robustness of linear resistivity.

Findings

Linear-in-temperature resistivity persists at low temperatures.

Hall angle does not show strange-metal signatures.

Random interactions support linear transport phenomena.

Abstract

Strange metals exhibit linear resistivity and anomalous Hall transport, yet a comprehensive theory that accounts for both phenomena is still lacking. Recent studies have shown SYK-like spatially random couplings between a Fermi surface and a bosonic field, either scalar or vector type, can yield linear-$T$ resistivity. In this paper, we continue the investigation on a vector coupling in the presence of a magnetic field. We compute the fermion and boson propagators, along with the self-energy and polarization functions, and determine their dependence on the magnetic field. Although the Hall angle does not exhibit the signature of strange-metal, the linear-in-temperature resistivity remains at low temperatures. Results indicate that random interactions can robustly support linear transport, though additional ingredients may be required to capture the full phenomenology of strange metals.