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Interference of Holon Strings in 2D Hubbard Model

The 2D Hubbard model with large repulsion is a central and yet unsolved problem in condensed matter physics for decades. The challenge appears below half filling, where the system is a doped antiferromagnet. In this regime, the fermion excitations are nothing like those in a Fermi liquid, which carry both spin and charge. Rather, they split up into holons and spinons, carrying charge and spin separately. Moreover, the motion of a holon is believed to stir up the underlying antiferromagnetic order, leaving behind it a string of "wrong" spins. While direct observation of the holon string is difficult in electron systems, it has become possible in cold atom experiments due to recent experimental advances. Here, we point out the key feature of the holon strings, i.e. its Marshall phase, can be observed through measurements of spin correlations. Moreover, the interference of these strings leads to an anisotropic holon propagation clearly distinguishable than those of spinless fermions, as well as a large suppression of the magnetic order in the region swept through by the strings, as if the system is driven towards a spin liquid. We further illustrate the effect of the Marshall phase by showing the motion of a holon in the so-called $σtJ$-model where the Marshall phase is removed.