Non self-conjugate strings, singular strings and rigged configurations in the Heisenberg model. (3rd February 2015)

• Record Type: Journal Article
• Authors: Deguchi, Tetsuo; Giri, Pulak Ranjan
• Is Part Of: Journal of statistical mechanics. (2015:Feb.)
• Publication Date: 2015-02-03
• Subjects: 1; 1/010 -- 1/070 -- 1/100 -- 1/130; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/2015/02/P02004
• Languages: English
• ISSNs: 1742-5468

Abstract

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.