Variational wavefunction for Mott insulator at finite $U$ using ancilla qubits

The Mott regime with finite $U$ offers a promising platform for exploring novel phases of matter, such as quantum spin liquids (QSL) that exhibit fractionalization and emergent gauge field. Here, we provide a new class 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 $\Phi$ tuning the charge gap. As $\Phi \rightarrow\infty$, the wavefunction reduces to the Gutzwiller projected state, while at $\Phi=U/2$, 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 novel conceptual framework and a powerful numerical tool for understanding Mott physics.