1999/10/04 by Eugene H. Kim, Gábor Fáth, G. Fath +3 · 117 citations
Mathematics · Physics and Astronomy · #Combinatorics #Condensed matter physics #Electron #Isotropy #Mathematics #Phase transition #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum many-body systems #Quantum mechanics #Renormalization group #Theoretical and Computational Physics #Theoretical physics #Topological order #Topology (electrical circuits) #Universality (dynamical systems) #Valence bond theory #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.62.14965
published in Physical review. B, Condensed matter 62(22), 14965-14974 (American Physical Society) · 11 pages, 16 postscript figures
arxiv created 1999/10/04 · openalex publication_date 2000/12/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider various two-leg ladder models exhibiting gapped phases. All of these phases have short-ranged valence bond ground states, and they all exhibit string order. However, we show that short-ranged valence bond ground states divide into two topologically distinct classes, and as a consequence, there exist two topologically distinct types of string order. Therefore, not all gapped phases belong to the same universality class. We show that phase transitions occur when we interpolate between models belonging to different topological classes, and we study the nature of these transitions.