# Duality between disordered nodal semimetals and systems with power-law hopping

## TL;DR

This paper reveals a duality between disordered nodal semimetals and systems with power-law hopping, enabling the transfer of theoretical insights and discovering new disorder-driven transitions distinct from Anderson localization.

## Contribution

The authors establish an exact mapping between low-energy theories of semimetals and systems with power-law interactions, unveiling novel disorder-driven phase transitions for long-range hopping systems.

## Key findings

- Duality mapping between semimetals and power-law hopping systems
- Existence of a new class of disorder-driven transitions for $rac{d}{2}<\gamma<d$
- Identification of non-Anderson disorder transitions in long-range systems

## Abstract

Nodal semimetals (e.g. Dirac, Weyl and nodal-line semimetals, graphene, etc.) and systems of pinned particles with power-law interactions (trapped ultracold ions, nitrogen defects in diamonds, spins in solids, etc.) are presently at the centre of attention of large communities of researchers working in condensed-matter and atomic, molecular and optical physics. Although seemingly unrelated, both classes of systems are abundant with novel fundamental thermodynamic and transport phenomena. In this paper, we demonstrate that low-energy field theories of quasiparticles in semimetals may be mapped exactly onto those of pinned particles with excitations which exhibit power-law hopping. The duality between the two classes of systems, which we establish, allows one to describe the transport and thermodynamics of each class of systems using the results established for the other class. In particular, using the duality mapping, we establish the existence of a novel class of disorder-driven transitions in systems with the power-law hopping $\propto1/r^\gamma$ of excitations with $d/2<\gamma<d$, different from the conventional Anderson-localisation transition. Non-Anderson disorder-driven transitions have been studied broadly for nodal semimetals, but have been unknown, to our knowledge, for systems with long-range hopping (interactions) with $\gamma<d$.