On-Shell Methods for Quantum Matter: Strongly correlated Dirac materials

TL;DR

This paper introduces a novel on-shell scattering amplitude framework to analyze strongly correlated Dirac materials, enabling efficient computation of physical observables like nonlinear Hall responses without complex Feynman diagrams.

Contribution

It applies on-shell amplitude methods to quantum matter, providing a new analytical approach for strongly correlated relativistic systems in condensed matter physics.

Findings

Derived nonlinear Hall conductivity from a single three-photon amplitude.

Demonstrated the efficiency of amplitude methods over traditional Feynman diagram calculations.

Showcased the potential of on-shell techniques for complex quantum materials.

Abstract

We propose a framework for applying on-shell scattering amplitude methods to emergent relativistic phases of quantum matter. Many strongly correlated systems, from Dirac and Weyl semimetals to topological-insulator surfaces, exhibit low-energy excitations that are effectively massless relativistic spinors. We show that physical observables such as nonlinear optical and Hall responses can be obtained from compact on-shell amplitudes, bypassing the complexity of Feynman diagrams. As a concrete demonstration, we derive the nonlinear Hall conductivity of a Dirac semimetal from a single parity-odd three-photon amplitude, highlighting the analytic and conceptual power of amplitude-based approaches for strongly correlated condensed-matter systems.