Table 1.
Numerical solutions of the BAEs (3.17), where $2N=4$, $\eta =0.6$, $a=1.3{\rm{i}}$, ${\xi }_{+}=0.3$, ${\xi }_{-}=1.8$, n indicates the number of energy levels and En is the corresponding energy. The energy En calculated from the Bethe roots is exactly the same as that obtained from the exact diagonalization of the Hamiltonian (2.1)."
| ${\mu }_{1}$ | ${\mu }_{2}$ | ${\mu }_{3}$ | ${\mu }_{4}$ | En | n |
|---|
| $-0.3000+1.1177{\rm{i}}$ | $-0.3000+1.3567{\rm{i}}$ | ⋯ | ⋯ | −9.3206 | 1 |
| $-0.6920-0.5799{\rm{i}}$ | $-0.6920+0.5799{\rm{i}}$ | $-0.3000+1.3595{\rm{i}}$ | ⋯ | −5.3779 | 2 |
| $-0.3000+0.5769{\rm{i}}$ | $-0.3000+1.3715{\rm{i}}$ | ⋯ | ⋯ | −4.6013 | 3 |
| $-0.6958-0.6407{\rm{i}}$ | $-0.6958+0.6407{\rm{i}}$ | $-0.3000-1.1392{\rm{i}}$ | ⋯ | −3.2736 | 4 |
| $-0.3000+0.5994{\rm{i}}$ | $-0.3000+1.1743{\rm{i}}$ | ⋯ | ⋯ | −3.1533 | 5 |
| $-0.3000-1.3867{\rm{i}}$ | ⋯ | ⋯ | ⋯ | −2.5986 | 6 |
| $-0.3000-1.2109{\rm{i}}$ | ⋯ | ⋯ | ⋯ | −1.7460 | 7 |
| $-0.6001-1.1974{\rm{i}}$ | $-0.6001+1.1974{\rm{i}}$ | ⋯ | ⋯ | 0.5545 | 8 |
| $-0.9231-0.7838{\rm{i}}$ | $-0.9231+0.7838{\rm{i}}$ | $-0.3000-0.8309{\rm{i}}$ | ⋯ | 2.1627 | 9 |
| $-0.3000-0.9609{\rm{i}}$ | ⋯ | ⋯ | ⋯ | 2.1688 | 10 |
| $-0.5752-0.8182{\rm{i}}$ | $-0.5752+0.8182{\rm{i}}$ | ⋯ | ⋯ | 2.1989 | 11 |
| −1.4562 | −0.9176 | $-0.3000+0.0712{\rm{i}}$ | 1.8613 | 3.7768 | 12 |
| −1.4094 | −0.9430 | $-0.3000+0.1085{\rm{i}}$ | ⋯ | 3.8209 | 13 |
| $-0.6644-0.2051{\rm{i}}$ | $-0.6644+0.2051{\rm{i}}$ | ⋯ | ⋯ | 4.1002 | 14 |
| $-0.3000-0.4181{\rm{i}}$ | ⋯ | ⋯ | ⋯ | 4.8439 | 15 |
| ⋯ | ⋯ | ⋯ | ⋯ | 6.4448 | 16 |
),Junpeng Cao1,2,3,4,(
