Condensed Matter

Topological aspects of physical systems, including the called topological states of matter, have become hot topics in the frontiers of physics in recent years. Here I would like to present a mathematically "popular" talk for professional physicists for a highlight or overview of how one can systematize knowledge of topological aspects of quantum field theories. Our starting points are Descent Equations and Gauge Structure in Configuration Space in Field Theory. (The audience needs only to know the meaning of "differential forms".)

In this talk, I will present our latest results on the development of algorithms for computer simulations based on tensor network states (TNS). The major part of this talk is concerned with finite projected entangled pair states (PEPS) in 2D: I will discuss their algorithmic properties as well as their performance for typical benchmark Hamiltonians [1, 2]. A minor part of this talk deals with the question whether TNS methods can be useful for density functional theory (DFT).

[1] M. Lubasch, J. I. Cirac, and M.-C. Ba\~{n}uls, New J. Phys. \textbf{16}, 033014 (2014).

[2] M. Lubasch, J. I. Cirac, and M.-C. Ba\~{n}uls, Phys. Rev. B \textbf{90}, 064425 (2014).