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.

Figure 1

The elementary processes introduced by the kinetic term in Eq. (11). The dashed arrows indicate the hopping of electrons. (a), (b) $H_t$ creates or annihilates a chargon pair. (c), (d) $H_t$ moves a doublon or a holon.

Figure 2

(a) The exchange of two spin-$\uparrow$ electrons induces the exchange of two holes, thus $P_{\uparrow }^e\left[c\right]=P_h\left[c\right]=1$. (b) In terms of partons, the process involves the exchange of two holons, $P_h\left[c\right]=1$, while in terms of electrons, $P_{\uparrow }^e\left[c\right]=1$.