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Unveiling the microscopic origins of quantum phases dominated by theinterplay of spin and motional degrees of freedom constitutes one of thecentral challenges in strongly correlated many-body physics. When holes movethrough an antiferromagnetic spin background, they displace the positions ofspins, which in turn induces effective frustration in the magnetic environment.However, a concrete characterization of this effect in a quantum many-bodysystem is still an unsolved problem. Here we introduce a Hamiltonianreconstruction scheme that allows for a precise quantification ofhole-motion-induced frustration. In particular, we access non-local correlationfunctions through projective measurements of the many-body state, from whicheffective spin-Hamiltonians can be recovered after detaching the magneticbackground from dominant charge fluctuations. The scheme is applied to systemsof mixed dimensionality, where holes are restricted to move in one dimension(1D), but $\mathrm{SU}(2)$ superexchange is two-dimensional (2D). Wedemonstrate that hole motion drives the spin background into a highlyfrustrated spin liquid regime, reminiscent of Anderson's resonating valencebond paradigm in doped cuprates. We exemplify the direct applicability of thereconstruction scheme to ultracold atom experiments by recovering effectivespin-Hamiltonians of experimentally obtained 1D Fermi-Hubbard snapshots. Ourmethod can be generalized to fully 2D systems, enabling an unprecedentedmicroscopic perspective on the doped Hubbard model.

Quantifying hole-motion-induced frustration in doped antiferromagnets by Hamiltonian reconstruction