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Exact solution of the quantum spin chains associated with the $sp(4)$ algebra | | Guang-Liang Li
; Junpeng Cao
; Panpan Xue
; Zhi-Rong Xin
; Kun Hao
; Wen-Li Yang
; Kangjie Shi
; Yupeng Wang
; | | Date: |
10 Dec 2018 | | Abstract: | The off-diagonal Bethe ansatz method is generalized to the integrable model
associated with the $sp(4)$ (or $C_2$) Lie algebra. By using the fusion
technique, we obtain the complete operator product identities among the fused
transfer matrices. These relations, together with some asymptotic behaviors and
values of the transfer matrices at certain points, enable us to determine the
eigenvalues of the transfer matrices completely. For the model with the
periodic boundary condition, the eigenvalues are described by homogeneous $T-Q$
relations, which coincides with those obtained by the conventional Bethe ansatz
methods. For the model with the off-diagonal boundary condition, the
eigenvalues are given in terms of inhomogeneous $T-Q$ relations, which is due
to the fact of the $U(1)$-symmetry-broken and also has failed to be obtained by
the conventional Bethe ansatz methods for many years. The method and the
results in this paper can be used to study other integrable models associated
with the $sp(2n)$ (i.e., $C_n$) algebra with a generic $n$. | | Source: | arXiv, 1812.3618 | | Services: | Forum | Review | PDF | Favorites | |
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