通过哈密顿量重构量化掺杂反铁磁体中空穴运动诱导的阻挫
Quantifying hole-motion-induced frustration in doped antiferromagnets by Hamiltonian reconstruction
AI总结：
本文提出哈密顿量重构方案，通过投影测量非局域关联函数并分离电荷涨落，精确量化掺杂反铁磁体中空穴运动诱导的阻挫，并在混合维度及一维Fermi-Hubbard实验数据中验证其有效性。
摘要：
揭示由自旋与运动自由度相互作用主导的量子相的微观起源，是强关联多体物理中的核心挑战之一。当空穴在反铁磁自旋背景中运动时，会移动自旋的位置，从而在磁环境中诱导出有效的阻挫。然而，在量子多体系统中对这一效应进行具体刻画仍是一个未解决的问题。本文提出了一种哈密顿量重构方案，能够精确量化空穴运动诱导的阻挫。我们通过对多体态进行投影测量来获取非局域关联函数，在将磁背景与主导的电荷涨落分离后，可以恢复出有效的自旋哈密顿量。该方案被应用于混合维度系统，其中空穴被限制在一维运动，但SU(2)超交换是二维的。我们证明，空穴运动将自旋背景驱动到高度阻挫的区域，并且该区域可以定量地由一个有效的J1-J2型自旋模型描述。我们通过从实验获得的一维Fermi-Hubbard快照中恢复有效自旋哈密顿量，例证了该重构方案在超冷原子实验中的适用性。我们的方法可以推广到完全二维系统，为掺杂Hubbard模型提供有前景的微观视角。
英文摘要：
Unveiling the microscopic origins of quantum phases dominated by the interplay of spin and motional degrees of freedom constitutes one of the central challenges in strongly correlated many-body physics. When holes move through an antiferromagnetic spin background, they displace the positions of spins, which induces effective frustration in the magnetic environment. However, a concrete characterization of this effect in a quantum many-body system is still an unsolved problem. Here we present a Hamiltonian reconstruction scheme that allows for a precise quantification of hole-motion-induced frustration. We access non-local correlation functions through projective measurements of the many-body state, from which effective spin-Hamiltonians can be recovered after detaching the magnetic background from dominant charge fluctuations. The scheme is applied to systems of mixed dimensionality, where holes are restricted to move in one dimension, but SU(2) superexchange is two-dimensional. We demonstrate that hole motion drives the spin background into a highly frustrated regime, which can quantitatively be described by an effective $J_1-J_2-$type spin model. We exemplify the applicability of the reconstruction scheme to ultracold atom experiments by recovering effective spin-Hamiltonians of experimentally obtained 1D Fermi-Hubbard snapshots. Our method can be generalized to fully 2D systems, enabling promising microscopic perspectives on the doped Hubbard model.
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