Revealing hidden antiferromagnetic correlations in doped Hubbard chains via string correlators


Spin-charge separation in atomic chains Strongly interacting electrons lined up along a string can experience the so-called spin-charge separation, where the electrons “split” into effective carriers of spin and charge, which then move independently. This phenomenon has been observed, somewhat indirectly, in solids. Hilker et al. show spin-charge separation in a direct way by using a one-dimensional (1D) array of cold atoms, playing the role of electrons, whose degrees of freedom of spin and charge can be monitored using a fermionic quantum gas microscope. Empty sites in the 1D lattice moved freely without disturbing the underlying antiferromagnetic order. Science , this issue p. 484 , A fermionic quantum gas microscope is used to track spin-charge separation in chains of 6 Li atoms. , Topological phases, like the Haldane phase in spin-1 chains, defy characterization through local order parameters. Instead, nonlocal string order parameters can be employed to reveal their hidden order. Similar diluted magnetic correlations appear in doped one-dimensional lattice systems owing to the phenomenon of spin-charge separation. Here we report on the direct observation of such hidden magnetic correlations via quantum gas microscopy of hole-doped ultracold Fermi-Hubbard chains. The measurement of nonlocal spin-density correlation functions reveals a hidden finite-range antiferromagnetic order, a direct consequence of spin-charge separation. Our technique, which measures nonlocal order directly, can be readily extended to higher dimensions to study the complex interplay between magnetic order and density fluctuations.