  Weak Mott regime with finite U is a wonderful region to search for quantum
spin liquid, but it is challenging to write down a wavefunction capturing both
spin liquid and charge fluctuations. Conventional methods using complicated
Jastrow factors have difficulties when the underlying spin liquid has a
non-trivial projective symmetry group (PSG). To cure this problem, here we
provide a new class wavefunction for Mott insulator through quantum
teleportation using ancilla qubits. We primarily focus on half filling of the
fermionic Hubbard model. We will prove that a single variation parameter $\Phi$
in our wavefunction tunes the Mott charge gap continuously. On a generic
lattice, we show that the wavefunction at $\Phi=+\infty$ recovers the familiar
Gutzwiller projectived wavefunction at infinite U. The wavefunction at
$\Phi=\frac{U}{2}$ is equivalent to applying the inverse Schrieffer Wolff
transformation at linear order of $t/U$, as expected in large but finite U
regime. From a gauge theory description we can show that the wavefunction has
an electronic sector decoupled from a spinon sector describing localized spin
moments. The charge gap $\Delta_c$ can be shown to be $2\Phi$ and we conjecture
that the wavefunction works well down to the regime with small charge gap on a
generic lattice. We represent the wavefunction using tensor network and
numerically confirm this conjecture in one dimension. Beyond the numerical
power, the ancilla wavefunction also provides a new conceptual picture to
understand the bandwidth tuned metal insulator transition. In this new
framework, there can in principle exist a narrow region of fractional Fermi
liquid (FL*) phase between the usual Fermi liquid and the Mott insulator, a
scenario which is not captured by the conventional slave rotor theory and thus
was usually outlooked.
