New families of non-parity-time-symmetric complex potentials with all-real spectra are derived by the supersymmetry method and the pseudo-Hermiticity method. With the supersymmetry method, we find families of non-parity-time-symmetric complex partner potentials which share the same spectrum as base potentials with known real spectra, such as the (complex) Wadati potentials. Different from previous supersymmetry derivations of potentials with real spectra, our derivation does not utilize discrete eigenmodes of base potentials. As a result, our partner potentials feature explicit analytical expressions which contain free functions. With the pseudo-Hermiticity method, we derive a new class of non-parity-time-symmetric complex potentials with free functions and constants, whose eigenvalues appear as conjugate pairs. This eigenvalue symmetry forces the spectrum to be all-real for a wide range of choices of these functions and constants in the potential. Tuning these free functions and constants, phase transition can also be induced, where conjugate pairs of complex eigenvalues emerge in the spectrum.

中文翻译：

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具有全实谱的非奇偶时间对称复势的新族

通过超对称方法和伪厄米性方法推导出具有全实谱的非奇偶时间对称复势的新族。使用超对称方法，我们找到了非奇偶时间对称复杂伙伴电位的家族，它们与具有已知真实光谱的基础电位共享相同的光谱，例如（复杂的）Wadati 电位。与先前具有真实光谱的势的超对称推导不同，我们的推导不利用基势的离散本征模。因此，我们的合作伙伴潜力具有包含自由函数的显式分析表达式。使用伪厄米性方法，我们推导出一类新的具有自由函数和常数的非奇偶时间对称复势，其特征值显示为共轭对。这种特征值对称性迫使谱对于这些函数和势中常数的广泛选择是全实的。调整这些自由函数和常数，也可以诱导相变，其中复杂特征值的共轭对出现在频谱中。