Yukawa-Lorentz Symmetry in Non-Hermitian Dirac Materials

TL;DR

This paper introduces a framework for non-Hermitian Dirac semimetals with Lorentz symmetry, exploring their phase transitions, emergent symmetries, and potential for novel quantum states in correlated materials.

Contribution

It presents a novel class of non-Hermitian Dirac semimetals with Lorentz invariance, analyzing their phase transitions, symmetry properties, and implications for quantum materials.

Findings

Real or imaginary linear band dispersion with zero density of states

Quantum phase transition to a non-Fermi liquid insulator under strong interactions

Emergent Yukawa-Lorentz symmetry in the quantum-critical regime

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.