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

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 $\text{not freezing}$. 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.

arXiv comment16 pages, 18 figures

References in corpus (38)

• Anyons in an exactly solved model and beyond
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Anderson Transitions
• Kwant: a software package for quantum transport
• The Kernel Polynomial Method
• Quantum Orders and Symmetric Spin Liquids
• Zoo of quantum-topological phases of matter
• Disorder Induced Localized States in Graphene
• Physics of the Kitaev model: fractionalization, dynamical correlations, and material connections
• Electron transport in disordered graphene
• On the stability of U(1) spin liquids in two dimensions
• Statistics and Scaling in Disordered Mesoscopic Electron Systems
• gl(N|N) Super-Current Algebras for Disordered Dirac Fermions in Two Dimensions
• Many-body spin Berry phases emerging from the $\pi$-flux state: antiferromagnetic/valence-bond-solid competition
• Gaussian field theories, random Cantor sets and multifractality
• Charged fermions coupled to ${\mathbb{Z}}_2$ gauge fields: Superfluidity, confinement and emergent Dirac fermions
• Particle-hole symmetric localization in two dimensions
• Orthogonal Metals: The simplest non-Fermi liquids
• Confinement transition of ${\mathbb{Z}}_2$ gauge theories coupled to massless fermions: emergent QCD${}_3$ and $SO(5)$ symmetry
• Ballistic transport in disordered graphene
• Disordered Critical Wave functions in Random Bond Models in Two Dimensions -- Random Lattice Fermions at $E=0$ without Doubling
• Density of states for the $\pi$-flux state with bipartite real random hopping only: A weak disorder approach
• Quantum spin liquid at finite temperature: proximate dynamics and persistent typicality
• Simple ${\mathbb{Z}}_2$ lattice gauge theories at finite fermion density
• Metal-insulator transition in 2D random fermion systems of chiral symmetry classes
• The integer quantum Hall plateau transition is a current algebra after all
• Multifractality and Conformal Invariance at 2D Metal-Insulator Transition in the Spin-Orbit Symmetry Class
• Density of states in graphene with vacancies: midgap power law and frozen multifractality
• Zero-energy states bound to a magnetic pi-flux vortex in a two-dimensional topological insulator
• Vacancy-induced low-energy states in undoped graphene
• Soluble limit and criticality of fermions in Z2 gauge theories
• Vacancies in Graphene : Dirac Physics and Fractional Vacuum Charges
• High-resolution real-space evaluation of the self-energy operator of disordered lattices: Gade singularity, spin-orbit effects and p-wave superconductivity
• Metal-insulator transition in a 2D system of chiral unitary class
• Disordered Electrons in a Strong Magnetic Field: Transfer Matrix Approaches to the Statistics of the Local Density of States
• Band-center metal-insulator transition in bond-disordered graphene
• Obstructed Atomic Insulators and Superfluids of Fermions Coupled to ${\mathbb{Z}}_2$ Gauge Fields
• Transport in honeycomb lattice with random $\pi$-fluxes: implications for low-temperature thermal transport in the Kitaev spin liquids