The Mott regime with finite $U$ offers a promising platform for exploring phases of matter, such as quantum spin liquids (QSL) that exhibit fractionalization and emergent gauge field. Here, we provide a wavefunction, dubbed ancilla wavefunction, to capture both charge and spin (gauge) fluctuations in QSLs at finite $U$. The ancilla wavefunction can unify the Fermi liquid and Mott insulator phases with a single variation parameter $\mathrm{\Phi }$ tuning the charge gap. As $\mathrm{\Phi }\to \infty$, the wavefunction reduces to the Gutzwiller-projected state, while at $\mathrm{\Phi }=U/2$, it is effectively equivalent to applying an inverse Schrieffer-Wolff transformation to the Gutzwiller-projected state. This wavefunction can be numerically simulated in the matrix product state representation, and its performance is supported by numerical results for both one- and two-dimensional Hubbard models. Besides, we propose the possibility of a narrow regime of fractional Fermi-liquid phase between the usual Fermi liquid and the Mott insulator phases close to the metal-insulator transition, a scenario typically overlooked by the conventional slave rotor theory. Our ancilla wavefunction offers a conceptual framework and a powerful numerical tool for understanding Mott physics.

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• High-temperature superconductors
• Mott insulators
• Quantum many-body systems
• Strongly correlated systems
• Hubbard model
• Tensor network methods
• Trial wave functions
• Variational wave functional methods