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

Abstract

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.

arXiv comment8 pages main text + 4 pages appendices, 2 figures; v2: accepted by Phys. Rev. B

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• On the possibility of many-body localization in a doped Mott insulator
• Nature of a single doped hole in two-leg Hubbard and $t$-$J$ ladders
• Spin and charge modulations in a single hole doped Hubbard ladder -- verification with optical lattice experiments
• Charge-spin mutual entanglement: A case study by exact diagonalization of the one hole doped $t$-$J$ loop
• Phenomenological Single-Particle Green's Function for the Pseudogap and Superconducting Phases of High-T${}_c$ Cuprates
• Spin Texture in Doped Mott Insulators with Spin-Orbit Coupling
• Thermal Hall Effect and Neutral Spinons in a Doped Mott Insulator
• Continuous transition from a Landau quasiparticle to a neutral spinon
• Mottness, Phase String, and High-$T_c$ Superconductivity
• Effect of phase string on single-hole dynamics in the two-leg Hubbard ladder