Non Self-conjugate Strings, Singular Strings and Rigged Configurations in the Heisenberg Model

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 making 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^2-6N+8)/8 singular solutions for M=6, M=7 down-spins in an even-length chain with N \geq 2M. Correspondence of the non self-conjugate string solutions and the singular string solutions to the rigged configurations has also been shown.

17 pages, 3 figures, published version

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• Excitations in the Yang-Gaudin Bose gas
• Exact quantum numbers of collapsed and non-collapsed 2-string solutions in the Heisenberg spin chain
• Singular eigenstates in the even(odd) length Heisenberg spin chain
• Truncated string state space approach and its application to nonintegrable spin-$\frac{1}{2}$ Heisenberg chain
• Heisenberg model and Rigged Configurations
• Exact regimes of collapsed and extra two-string solutions in the two down-spin sector of the spin-1/2 massive XXZ spin chain
• Bethe's Quantum Numbers And Rigged Configurations
• Rigged Configurations Approach For The Spin-1/2 Isotropic Heisenberg Model