High-resolution real-space evaluation of the self-energy operator of disordered lattices: Gade singularity, spin-orbit effects and p-wave superconductivity

Abstract

Disorder is a prominent factor influencing the fate of condensed phases of matter, yet the true extent of its impact is generally difficult to understand due to the significant role played by quantum interference effects, entanglement between internal spin and orbital degrees of freedom, and proximity to quantum critical points. Here we show that the quasiparticle self-energy-a direct probe of the renormalization of low-energy excitations due to interactions and disorder-can be obtained by means of unbiased, general-purpose polynomially-scaling spectral expansions of lattice Green's functions. Our scheme provides a powerful framework to access the disorder self-energy Σ(k, ω) in unprecedented large tight-binding systems [with up to billions of orbitals (N ≈ 10 9 )] with energy resolution only limited by the mean level spacing. We demonstrate the versatility of our approach in 3 distinct problems: (i) the Gade singularity in the honeycomb lattice with vacancy defects; (ii) impurity resonances in a spin-orbit-coupled ferromagnet and (iii) mixed s-wave and p-wave superconductivity in disordered graphene. Our study unravels striking manifestations of nonperturbative quantum interference effects so far inaccessible to real-space numerical techniques.