On integrable matrix product operators with bond dimension D = 4. (6th January 2015)

• Record Type: Journal Article
• Authors: Katsura, Hosho
• Is Part Of: Journal of statistical mechanics. (2015:Jan.)
• Publication Date: 2015-01-06
• Subjects: 1 -- 2; 1/010 -- 1/070 -- 1/130 -- 2/115; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/2015/01/P01006
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: We construct and study a two-parameter family of matrix product operators of bond dimension D = 4. The operators M ( x, y ) act on, i.e. the space of states of a spin-1/2 chain of length N . For the particular values of the parameters: x = 1/3 and, the operator turns out to be proportional to the square root of the reduced density matrix of the valence-bond-solid state on a hexagonal ladder. We show that M ( x, y ) has several interesting properties when ( x, y ) lies on the unit circle centered at the origin: x 2 + y 2 = 1. In this case, we find that M ( x, y ) commutes with the Hamiltonian and all the conserved charges of the isotropic spin-1/2 Heisenberg chain. Moreover, M ( x 1, y 1 ) and M ( x 2, y 2 ) are mutually commuting if for both i = 1 and 2. These remarkable properties of M ( x, y ) are proved as a consequence of the Yang–Baxter equation.