Berlin 2018 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 72: Poster: Stoch. and Nonl. Dy., Modeling, Compl. Sys.
DY 72.12: Poster
Thursday, March 15, 2018, 15:30–18:00, Poster A
Chain and ladder models with two-body interactions and analytical ground states — Sourav Manna1 and •Anne E. B. Nielsen2 — 1Max-Planck-Institut für Physik komplexer Systeme, D-01187 Dresden, Germany — 2Max-Planck-Institut für Physik komplexer Systeme, D-01187 Dresden, Germany
We consider a family of spin-1/2 models with few-body, SU(2) invariant Hamiltonians and analytically known ground states related to the Haldane-Shastry (HS) wavefunction. The spins are placed on the surface of a cylinder, and the standard HS model is obtained by placing the spins with equal spacing in a circle around the cylinder. Here, we show that another interesting family of models with two-body exchange interactions is obtained if we instead place the spins along one or two lines parallel to the cylinder axis, giving rise to chain and ladder models, respectively. In this case, the circumference of the cylinder can be changed independently from the other length scales in the system, and we use Monte Carlo simulations and analytical investigations to study how the circumference affects the properties of the models. If the circumference is large compared to the other length scales in the system, we find that the two legs of the ladder decouple into two chains with HS-like properties, and if the circumference is small compared to the other length scales the wavefunction reduces to a product of singlets