Non self-conjugate strings, singular strings and rigged configurations in the Heisenberg model. (3rd February 2015) - Deguchi, Tetsuo; Giri, Pulak Ranjan
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.