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 center 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 Rapid Communication, we demonstrate that low-energy field theories of quasiparticles in semimetals may be mapped exactly onto those of pinned particles with power-law hopping excitations. The duality between the two classes of systems, which we establish, trades strong disorder in one class for weak disorder in the other, and 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 another class of disorder-driven transition in systems with the power-law hopping $\propto 1/r^{\gamma }$ of excitations with $d/2<\gamma <d$, different from the conventional Anderson-localization transition. Non-Anderson disorder-driven transitions have been studied broadly for nodal semimetals. Our work extends the class of systems exhibiting such transitions to systems with long-range hopping (interactions) with $\gamma <d$.

• Received 13 August 2019

DOI:https://doi.org/10.1103/PhysRevResearch.1.032035

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society