arXiv:1408.7030 · Journal of Statistical Mechanics Theory and Experiment

Non self-conjugate strings, singular strings and rigged configurations in the Heisenberg model

Tetsuo Deguchi, Pulak Ranjan Giri

Published Feb 3, 2015• 11 citations

Abstract

We observe a different type of complex solutions in the isotropic spin-1/2 Heisenberg chain starting from N = 12, where the central rapidity of some of the odd-length strings becomes complex so that not all the strings self-conjugate individually. We show that there are at most ( N − 2)/2 singular solutions for M = 4, M = 5 down-spins and at most ( N 2 − 6 N + 8)/8 singular solutions for M = 6, M = 7 down-spins in an even-length chain with N ⩾ 2 M . Correspondence of the non self-conjugate string solutions and the singular string solutions to the rigged configurations has also been shown.

DOI: 10.1088/1742-5468/2015/02/p02004

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