2000/09/18 by Bruno Nachtergaele
Physics and Astronomy · Mathematics · #math-ph #math.MP #msc:82B10 #msc:82B24 #msc:82D40
published as in {\it XIII International Congress of Mathematical Physics}, A. Grigoryan, A. Fokas, T. Kibble, B. Zegarlinski (Eds), International Press, Boston 2001, pp 243--249 · 7 pages, 1 figure (embedded eps). For the proceedings of the XIII International Congress of Mathematical Physics, London, July 18-24, 2000
arxiv created 2000/09/18 · arxiv updated 2009/11/30
This paper is a short review of recent results on interface states in the Falicov-Kimball model and the ferromagnetic XXZ Heisenberg model. More specifically, we discuss the following topics: 1) The existence of interfaces in quantum lattice models that can be considered as perturbations of classical models. 2) The rigidity of the 111 interface in the three-dimensional Falicov-Kimball model at sufficiently low temperatures. 3) The low-lying excitations and the scaling of the gap in the 111 interface ground state in the ferromagnetic XXZ Heisenberg model in three dimensions. 4) The existence of droplet states in the XXZ chain and their properties.