Fermion quantum Monte Carlo methods are a powerful tool to simulate materials and models. After introducing the method [1], I will concentrate on two subjects. The first one is experimentally driven, and concentrates on magnetic ad-adtoms on metallic surfaces [2]. Here we will show that phenomena such as Kondo breakdown transitions are achievable in these systems. In the second part of the talk, I will introduce a model in which the quantum spin Hall (QSH) state is dynamically generated. The key point of this state is that Skyrmions of the QSH order parameter carry charge 2e. This provides a novel route to superconcductivity [3] and new realizations of deconfined quantum critical points [4].
[1] ALF Collaboration, F. F. Assaad, M. Bercx, F. Goth, A. Goetz, J. S. Hofmann, E. Huffman, Z. Liu, F. Parisen Toldin, J. S. E. Portela, and J. Schwab, arXiv:2012.11914 (2021).
[2] B. Danu, M. Vojta, F. F. Assaad, and T. Grover, Phys. Rev. Lett. 125 (2020), 206602.
[3] Z. Wang, Y. Liu, T. Sato, M. Hohenadler, C. Wang, W. Guo, and F. F. Assaad, arXiv:2006.13239 (2020).
[4] Y. Liu, Z. Wang, T. Sato, M. Hohenadler, C. Wang, W. Guo, and F. F. Assaad, Nature Communications 10 (2019), no. 1, 2658.