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arXiv 2503.24331quant-phcond-mat.str-el
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利用具有RT对称性的非厄米自旋模型进行临界量子计量

Critical quantum metrology using non-Hermitian spin model with RT-symmetry

Keshav Das Agarwal, Tanoy Kanti Konar, Leela Ganesh Chandra Lakkaraju, Aditi Sen De

备注：
v1 : 7 pages, 3 figures; v2 : 9 pages, 4 figures, new results on dynamics added, references updated
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AI总结：

本研究证明具有RT对称性的非厄米iKSEA自旋模型在临界点和例外点实现海森堡标度，并在KSEA相互作用接近各向异性参数时达到超海森堡标度，为量子计量提供新途径。

摘要：

具有Kaplan-Shekhtman-Entin-Wohlman-Aharony (KSEA)相互作用且满足$\mathcal{RT}$对称性的非厄米横向$XY$模型（称为$iKSEA$模型）同时具备一个本征矢量重合的例外点和一个能隙闭合的量子临界点。为了精确估计系统的磁场，我们证明了$iKSEA$模型基态的量子Fisher信息（QFI）——它是均方根误差所量化的精度的下界——按$N^2$标度，其中$N$为系统尺寸。这在热力学极限下于量子临界点和例外点均提供了海森堡标度。这表明，当系统与浴接触时，储层工程可以提高系统参数的估计精度，从而产生这种非厄米模型。此外，我们解析地证明，与厄米系统相反，当KSEA相互作用的强度接近各向异性参数时，QFI超越海森堡极限并实现超海森堡标度（$\sim N^6$），允许非厄米性与厄米性特征之间的竞争，只要系统尺寸适中即可。此外，我们说明，从乘积态出发，非厄米演化哈密顿量可以在破缺区域产生超越标准量子极限的动力学态。

英文摘要：

The non-Hermitian transverse $XY$ model with Kaplan-Shekhtman-Entin-Wohlman-Aharony (KSEA) interaction having $\mathcal{RT}$-symmetry, referred to as $iKSEA$ model, possesses both an exceptional point at which eigenvectors coalesce and a quantum critical point where gap-closing occurs. To precisely estimate the magnetic field of the system, we prove that the quantum Fisher information (QFI) of the ground state of the $iKSEA$ model, which is a lower bound of the precision quantified by the root mean square error, scales as $N^2$, with $N$ being the system-size. This provides Heisenberg scaling both at the quantum critical point and the exceptional point in the thermodynamic limit. It indicates that reservoir engineering can provide enhanced precision of system parameters when the system is in contact with the bath, resulting in this non-Hermitian model. Additionally, we demonstrate analytically that, in contrast to Hermitian systems, QFI surpasses the Heisenberg limit and achieves super-Heisenberg scaling ($\sim N^6$), when the strength of the KSEA interaction approaches the anisotropy parameter, permitting competition between non-hermiticity and hermiticity features, as long as the system size is moderate. Moreover, we illustrate that starting from a product state, the non-Hermitian evolving Hamiltonian can create the dynamical state that surpasses the standard quantum limit in the broken regime.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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