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Physical review. B, Condensed matter

Complete solution of the antiferromagnetic Heisenberg rings withN=12–16 sites

K. Fabricius, U. Löw, K.-H. Mütter, P. Ueberholz

Published Oct 1, 1991• 32 citations
Publisher

Abstract

We present results of a complete and exact diagonalization of the antiferromagnetic Heisenberg Hamiltonian for rings with N=12, 13, 14, 15, or 16 sites.Received 17 April 1991DOI:https://doi.org/10.1103/PhysRevB.44.7476©1991 American Physical Society

DOI
10.1103/physrevb.44.7476

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We present results of a complete and exact diagonalization of the antiferromagnetic Heisenberg Hamiltonian for rings with N=12, 13, 14, 15, or 16 sites.Received 17 April 1991DOI:https://doi.org/10.1103/PhysRevB.44.7476©1991 American Physical Society
The construction of a complete set of stationary states of the linear Heisenberg system with periodic boundary conditions (rings) has been a topic of intensive research for many decades. Many eminent theoreticians have made their contribution to this joint eort, but we should mention in the rst place the epoch-making work of Bethe 1 and Hulthen. 5 Their work is the basis of many papers on this topic that have appeared during the past 70 years. We do no have the intention to give a complete survey of all this work but we will try to indicate that especially an asymptotic approach starting from the Hypothesis of Strings gives the prospect of a general and complete solution of the Heisenberg chain.