Speaker
Description
In condensed matter systems where translational invariance is inevitably or deliberately broken, probing local observables is paramount to addressing a wealth of intriguing phenomena, such as multifractality, quasiparticle interference and real-space orbital magnetic textures.
In this talk we show that the well-known computational bottleneck of computing local properties in non-periodic lattices of realistic sizes can be circumvented by the use of a novel, highly scalable real-space approach [1]. After demonstrating its significant advantages by benchmarking on the π-flux model with isolated and clustered defects, we extend our numerical framework to inhomogeneous correlated systems [2]. As a proof of concept, the method is used to investigate the local robustness of s-wave and p-wave superconducting phases in disordered graphene in a fully non-perturbative fashion. These results bring opportunities for the real-space simulation of non-periodic quantum phases of matter beyond previous approaches.
[1] Veiga, H. P., Pinheiro, D. R., Pires, J. P. Santos, & Lopes, J. M. Viana Parente. (2025). Markov Inequality as a Tool for Linear-Scaling Estimation of Local Observables. 10.48550/arxiv.2510.21688
[2] João, S. M., Viana Parente Lopes, J. M., & Ferreira, A. (2022). High-resolution real-space evaluation of the self-energy operator of disordered lattices: Gade singularity, spin–orbit effects and p-wave superconductivity. Journal of Physics: Materials, 5, 045002