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Nuclear Physics B

Exact solution of the C2(1) quantum spin chain with open boundary condition

Guang-Liang Li, Junpeng Cao, Yi Qiao, Kun Hao, Wen‐Li Yang

Published Jun 27, 2024• 1 citation
Publisher

Abstract

In this paper, we studied the exact solution of the C2(1) invariant quantum spin chain with off-diagonal open boundary condition. We obtain a solution of the reflection equation where the all matrix element of reflection matrix are nonzeros. By using the technique of fusion, we construct the fused transfer matrix and find the closed recursive relations among the transfer matrices. Based on the algebraic analysis, we obtain the eigenvalue of the system and express it as the inhomogeneous T−Q relation.

DOI
10.1016/j.nuclphysb.2024.116611

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We formulate a general fusion procedure for open gl(N)\mathfrak{gl}(N)gl(N) spin chains. We construct the fused boundary reflection matrices and the corresponding fused reflection equations. By using the intertwining relation between the fused reflection matrices and the fusion operator, we identify the invariant subspace of the fused reflection matrices carrying the irreducible representations of gl(N)\mathfrak{gl}(N)gl(N). We also construct the fused transfer matrix and evaluate it explicitly in the total tensor product space and the invariant subspaces. Finally, we demonstrate that the ABJM spin chain model originates from such fusion procedure and derive three classes of boundary reflection matrices solutions on the anti-fundamental representation space of su(4)\mathfrak{su}(4)su(4).