Numerical study of the t-J model in mixed dimensions

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 in turn induces effective frustration in the magnetic environment. This competition in paradigmatic Hamiltonians like the Fermi-Hubbard and t-J model gives rise to a plethora of many-body phases, many of which still lack microscopic understanding. In this talk, we present numerical studies of the t-J model in mixed dimension, where charge carriers are restricted to move only in one direction, whereas magnetic SU(2) interactions are two-dimensional. At low temperatures, we find that hidden spin correlations lead to a remarkably resilient stripe phase featuring incommensurate magnetic order. At elevated temperatures, where charge carries effectively move freely through the spin background, we use Hamiltonian reconstruction schemes to recover effective spin-Hamiltonians after detaching the magnetic background from dominant charge fluctuations. This enables us to precisely quantify the magnetic frustration in the spin background induced by the motion of the holes. We demonstrate that the spin background is driven into a highly frustrated spin liquid regime, reminiscent of Anderson's resonating valence bond paradigm in doped cuprates. With recent advances in quantum gas microscopy to mixed dimensions, our study enables an unprecedented microscopic perspective on the doped Hubbard model.