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Sign Structure, Electron Fractionalization, and Emergent Gauge Description of the Hubbard Model

The Fermi sign structure plays a crucial role for a Landau's Fermi liquid. In this work, we identify the exact sign structure for the bipartite Hubbard model at an arbitrary strength of the on-site Coulomb repulsion $U$. This general sign structure naturally reproduces the conventional fermion signs in the small $U$ limit, and the phase string signs of the $t$-$J$ model in the large $U$ limit. We focus on the half-filling case as an example to illustrate why such a generic sign structure is important to understand the transition from the weakly correlated Fermi liquid regime to the strongly correlated Mott regime. In particular, we show that an electron fractionalization scheme with emergent partons and mutual Chern-Simons gauge fields provides a suitable framework to accurately handle the singular sign structure in two dimensions. A ground state ansatz at half-filling with incorporating the sign structure and the specific electron fractionalization is also proposed.