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

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 $\propto 1/r^{\gamma }$ 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 $\gamma <d$.

4.3+1 pages, 2 figures

References in corpus (17)

• Many body localization and thermalization in quantum statistical mechanics
• Anderson Transitions
• Many-body localization, thermalization, and entanglement
• Topological Node-Line Semimetal in Three Dimensional Graphene Networks
• Weyl Semimetals, Fermi Arcs and Chiral Anomalies (A Short Review)
• Recent progress in many-body localization
• Chiral Anomaly and Diffusive Magnetotransport in Weyl Metals
• Experimental tests of the chiral anomaly magnetoresistance in the Dirac-Weyl semimetals Na${}_3$Bi and GdPtBi
• Rare region effects dominate weakly disordered 3D Dirac points
• Many-body localization transition with power-law interactions: Statistics of eigenstates
• Unconventional localisation transition in high dimensions
• Vanishing density of states in weakly disordered Weyl semimetals
• Consistent hydrodynamic theory of chiral electrons in Weyl semimetals
• Nodal points of Weyl semimetals survive the presence of moderate disorder
• Dynamo Effect and Turbulence in Hydrodynamic Weyl Metals
• New Quantum Transition in Weyl Semimetals with Correlated Disorder
• Energy-level statistics in strongly disordered systems with power-law hopping

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• Power-Duality in Path Integral Formulation of Quantum Mechanics