论文标题
通过Jordan-Wigner Transformation的强力二元性：使用费米子方法与$ su（2）$ spin Systems使用
Strong-Weak Duality via Jordan-Wigner Transformation: Using Fermionic Methods for Strongly Correlated $su(2)$ Spin Systems
论文作者
论文摘要
Jordan-Wigner Transformation建立了$ SU（2）$和费米金代数之间的双重性。我们提出了定性的论点和数值证据，即在将旋转旋转到费米子上时，转换使强大的相关性较弱，如哈特里福克的近似与转化的哈密顿量的近似所证明的那样。当转化为费米子时，可以根据降低自旋移动项的降低来合理化此结果。相反，将费米子映射到Qubits可以使强大的相关性更强，从而使其解决方案复杂化时，当人们使用基于量子的相关器时。弦乐操作员的存在对在古典计算机上实施量子化学方法构成了挑战，但是可以使用既定计算成本的既定技术来处理这些方法。我们对XXZ和J $ _1 $ -J $ -J $ _2 $ HEISENBERG（1D和2D）的原则结果证明表明，JW转换的Fermionic Hamiltonian在其相图的关键区域中降低了复杂性，并为解决挑战性的旋转问题提供了更好的起点。
The Jordan-Wigner transformation establishes a duality between $su(2)$ and fermionic algebras. We present qualitative arguments and numerical evidence that when mapping spins to fermions, the transformation makes strong correlation weaker, as demonstrated by the Hartree-Fock approximation to the transformed Hamiltonian. This result can be rationalized in terms of rank reduction of spin shift terms when transformed to fermions. Conversely, the mapping of fermions to qubits makes strong correlation stronger, complicating its solution when one uses qubit-based correlators. The presence of string operators poses challenges to the implementation of quantum chemistry methods on classical computers, but these can be dealt with using established techniques of low computational cost. Our proof of principle results for XXZ and J$_1$-J$_2$ Heisenberg (in 1D and 2D) indicate that the JW transformed fermionic Hamiltonian has reduced complexity in key regions of their phase diagrams, and provides a better starting point for addressing challenging spin problems.
