Quantum Monte Carlo methods can be used to obtain unbiased information about the properties of models for strongly correlated electrons. In this project, we will develop and apply such methods to different physical systems which have in common a significant spin-orbit and electron-electron interaction. Whereas the study of electronic correlation effects has a long history in condensed matter physics, the exploration of the interplay between correlations and spin-orbit coupling has begun more recently, and was boosted by the discovery of topological superconductors and insulators.
We will investigate (i) candidate models for interaction-generated topological superconductors with spin-orbit coupling, (ii) models of quantum spin Hall and topological Kondo insulators, (iii) models for isolated or coupled correlated chains on substrates for which the breaking of inversion symmetry gives rise to a Rashba spin-orbit coupling. Whereas topological aspects play a key role for (i) and (ii), (iii) will focus on the experimentally observable effects of the substrate and the Rashba coupling. For (i) and (ii), it will be important to investigate both edge and bulk correlation effects, and to identify tools to characterize the topological states. For (iii), we will study the possible modifications of the low-energy physics when chains are coupled to other chains and/or the substrate in a setting with significant Rashba coupling.
The two complementary quantum Monte Carlo methods to be used will allow us to study two-dimensional and three-dimensional models on meaningfully large lattices. In particular, we will calculate single-particle spectral functions that can be compared to ARPES measurements, and transport properties.
[C01.4] M. Hohenadler, F. Parisen Toldin, I. F. Herbut, and F. F. Assaad, Phase diagram of the Kane-Mele-Coulomb model, Phys. Rev. B 90, 085146 (2014).