Yukawa-Lorentz Symmetry of Tilted Non-Hermitian Dirac Semimetals at Quantum Criticality

TL;DR

This paper demonstrates that Yukawa-Lorentz symmetry can emerge at quantum critical points in tilted non-Hermitian Dirac semimetals, with tilt effects becoming irrelevant near the criticality, supported by epsilon expansion analysis.

Contribution

It shows that tilt terms in non-Hermitian Dirac Hamiltonians are irrelevant at the quantum critical point, extending the understanding of emergent Lorentz symmetry in open quantum systems.

Findings

Tilt term becomes irrelevant near the QCP.

Velocity anisotropy also becomes irrelevant at the QCP.

Predictions can be tested via quantum Monte Carlo simulations.

Abstract

Dirac materials, hosting linearly dispersing quasiparticles at low energies, exhibit an emergent Lorentz symmetry close to a quantum critical point (QCP) separating semimetallic state from a strongly-coupled gapped insulator or superconductor. This feature appears to be quite robust even in the open Dirac systems coupled to an environment, featuring non-Hermitian (NH) Dirac fermions: close to a strongly coupled QCP, a Yukawa-Lorentz symmetry emerges in terms of a unique terminal velocity for both the fermion and the bosonic order parameter fluctuations, while the system can either retain non-Hermiticity or completely decouple from the environment thus recovering Hermiticity as an emergent phenomenon. We here show that such a Yukawa-Lorentz symmetry can emerge at the quantum criticality even when the NH Dirac Hamiltonian includes a tilt term at the lattice scale. As we demonstrate by performing a leading order $\epsilon=3-d$ expansion close to $d=3$ upper critical dimension of the theory, a tilt term becomes irrelevant close to the QCP separating the NH Dirac semimetal and a gapped (insulating or superconducting) phase. Such a behavior also extends to the case of the linear-in-momentum non-tilt perturbation, introducing the velocity anisotropy for the Dirac quasiparticles, which also becomes irrelevant at the QCP. These predictions can be numerically tested in quantum Monte Carlo lattice simulations of the NH Hubbard-like models hosting low-energy NH tilted Dirac fermions.