Critical States of Fermions with ${\mathbb{Z}}_2$ Flux Disorder

TL;DR

This paper uncovers a new class of critical, multifractal states in fermions on a square lattice with $ ext{Z}_2$ flux disorder, revealing complex transport and spectral properties that challenge existing theories.

Contribution

It introduces a novel critical phase of Dirac fermions with multifractal zero-energy states influenced by flux defect concentration and correlations, not captured by traditional RG methods.

Findings

Multifractal zero-energy states depend on flux defect concentration and correlations.

The multifractal spectrum exhibits termination but not freezing.

A universal relation between conductivity and Lyapunov exponent is established.

Abstract

Motivated by many contemporary problems in condensed matter physics where matter particles experience random gauge fields, we investigate the physics of fermions on a square lattice with $\pi$-flux (that realizes Dirac fermions at low energies), subjected to flux disorder arising from a random ${\mathbb{Z}}_2$ gauge field that results from the presence of flux defects (plaquettes with zero flux). At half-filling, where the system possesses BDI symmetry, we show that a new class of critical phases is realized, with the states at zero energy showing a multifractal character. The multifractal properties depend on the concentration $\mathfrak{c}$ of the $\pi$-flux defects and spatial correlations between the flux defects. These states are characterized by the singularity spectrum, Lyapunov exponents, and transport properties. For any concentration of flux defects, we find that the multi-fractal spectrum shows termination, but $\textit{not freezing}$. We characterize this class of critical states by uncovering a relation between the conductivity and the Lyapunov exponent, which is satisfied by the states irrespective of the concentration or the local correlations between the flux defects. We demonstrate that renormalization group methods, based on perturbing the Dirac point, fail to capture this new class of critical states. This work not only offers new challenges to theory, but is also likely to be useful in understanding a variety of problems where fermions interact with discrete gauge fields.