Quantum Fisher Information and Lee‐Yang Zeros with Quantum Coherence of the Isotropic XY$XY$ Model and the Energy Scale

Lee-Yang zeros lie on the complex plane of the control parameters for many-body systems with finite size, such as the transverse magnetic field and the inverse temperature. Here, an anisotropic spin system with nearest-neighbor interactions for finite-size parity space is considered. The Lee-Yang zeros are obtained in anisotropic XY$XY$ model for the complex plane of the transverse magnetic field and in the isotropic XY$XY$ model for the complex fugacity plane of the quantum coherence. A characteristic function to represent the probe spin coherence for the isotropic XY$XY$ model, and study on Lee-Yang zeros, quantum coherence, and quantum Fisher information at the complex fugacity plane is presented. The relationship between quantum Fisher information and quantum coherence in decoherence channels is demonstrated and it is illustrated that information cannot be acquired at high temperatures. Meanwhile, the ground-state energy on the complex plane for the anisotropic XY$XY$ model is studied and the free energy cumulants with the partition function of the anisotropic XY$XY$ model for parity space is calculated.