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The anisotropic spin-1/2 chains with arbitrary boundary fields arediagonalized with the off-diagonal Bethe ansatz method. Based on the propertiesof the R-matrix and the K-matrices, an operator product identity of thetransfer matrix is constructed at some special points of the spectralparameter. Combining with the asymptotic behavior (for XXZ case) or thequasi-periodicity properties (for XYZ case) of the transfer matrix, theextended T-Q ansatzs and the corresponding Bethe ansatz equations are derived.

Off-diagonal Bethe ansatz solutions of the anisotropic spin-1/2 chains with arbitrary boundary fields