Yukawa-Lorentz Symmetry in Non-Hermitian Dirac Materials

Abstract

Lorentz spacetime symmetry represents a unifying feature of the fundamental forces, typically manifest at sufficiently high energies, while in quantum materials it emerges in the deep low-energy regime. However, its fate in quantum materials coupled to an environment thus far remained unexplored. We here introduce a general framework of constructing symmetry-protected Lorentz invariant non-Hermitian (NH) Dirac semimetals (DSMs), realized by invoking masslike anti-Hermitian Dirac operators to its Hermitian counterpart. Such NH DSMs feature purely real or imaginary isotropic linear band dispersion, yielding a vanishing density of states. Dynamic mass orderings in NH DSMs thus take place for strong Hubbardlike local interactions through a quantum phase transition, hosting a non-Fermi liquid, beyond which the system becomes an insulator. We show that depending on the internal Clifford algebra between the NH Dirac operator and candidate mass order-parameter, the resulting quantum-critical fluid either remains coupled with the environment or recovers full Hermiticity by decoupling from the bath, while always enjoying an emergent Yukawa-Lorentz symmetry in terms of a unique terminal velocity. We showcase the competition between such mass orderings, their hallmarks on quasiparticle spectra in the ordered phases, and the relevance of our findings for correlated designer NH Dirac materials.

Published Version: 10 Pages, 3 Figures & 1 Table (Supplemental Material as Ancillary File)

References in corpus (25)

• The electronic properties of graphene
• Weyl and Dirac Semimetals in Three Dimensional Solids
• Quantum Gravity at a Lifshitz Point
• Data Tables for Lorentz and CPT Violation
• Dirac materials
• Non-Fermi liquid behaviour of electrons in the half-filled honeycomb lattice (A renormalization group approach)
• Observation of Non-Hermitian Skin Effect and Topology in Ultracold Atoms
• Quantum criticality between topological and band insulators in $(3+1)$-dimensions
• Masses in graphene-like two-dimensional electronic systems: topological defects in order parameters and their fractional exchange statistics
• Artificial graphene with tunable interactions
• Emergence of supersymmetry at a critical point of a lattice model
• A Classification of Non-Hermitian Random Matrices
• Theory of a quantum critical phenomenon in a topological insulator: (3+1)-dimensional quantum electrodynamics in solids
• Emergent Lorentz symmetry near fermionic quantum critical points in two and three dimensions
• Multi-critical behavior of $Z_2\times O(2)$ Gross-Neveu-Yukawa theory in graphene
• Emergent Lorentz invariance from Strong Dynamics: Holographic examples
• Non-Hermitian strongly interacting Dirac fermions: a quantum Monte-Carlo study
• Extended Hubbard model in undoped and doped monolayer and bilayer graphene: Selection rules and organizing principle among competing orders
• The emergence of a universal limiting speed
• From Birefringent Electrons to a Marginal or Non-Fermi Liquid of Relativistic Spin-1/2 Fermions: An Emergent Superuniversality
• Itinerant quantum multi-criticality of two dimensional Dirac fermions
• Optical conductivity of an interacting Weyl liquid in the collisionless regime
• Emergent chiral symmetry in a three-dimensional interacting Dirac liquid
• Shear viscosity as a probe of nodal topology
• Relativistic non-Fermi liquid from interacting birefringent fermions: A robust superuniversality

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• Yukawa-Lorentz Symmetry of Tilted Non-Hermitian Dirac Semimetals at Quantum Criticality
• Model non-Hermitian topological operators without skin effect: A general principle of construction
• Non-Hermitian catalysis of spontaneous symmetry breaking on Euclidean and hyperbolic lattices
• Axionic quantum criticality of generalized Weyl semimetals
• Zero modes and index theorems for non-Hermitian Dirac fermions
• Minimal Hamiltonian deformations as bulk probes of effective non-Hermiticity in Dirac materials
• Exceptional flat bands in bipartite non-Hermitian lattices
• Physical constraints on effective non-Hermitian systems