Entanglement Signatures of (2+1)D Dirac Fermions Subjected to Randomness

Abstract In this work, we investigate disordered Dirac fermions from the perspective of quantum entanglement, which provides a different angle compared to the ordinary perturbative renormalization group (RG) analysis. We consider Dirac fermions subjected to random hopping and random flux, which respectively fall into the chiral Gaussian orthogonal ensemble (cGOE) and chiral Gaussian unitary ensemble (cGUE) universality classes. Existing studies based on perturbative calculations suggest that both types of randomness are marginal. Here, through numerical simulations of the corresponding lattice models, we find that these two different types of randomness exhibit distinct entanglement features, signaling completely different properties in contrast to the perturbative RG analysis. In particular, although the entropy area-law is generally held for both types of randomness, we identify that the subleading term of the entanglement entropy is enhanced by random flux but not by random hopping. This subleading term is known as the entropic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="script">F</mml:mi> </mml:mrow> </mml:math> -function in the clean limit without disorder. Our observations indicate that disordered theories in cGOE and cGUE are essentially different, which recalls careful analysis on the RG calculations.