a variational wavefunction for weak Mott insulator and pseudogap metal using ancilla qubits*

Ancilla qubits wave function was proposed [Phys Rev R, 023172 (2020)] to describe the pseudogap phase in the hole doped cuprates. In the ansatz, the original physical layer is accompanied by two hidden layers, on which the ancilla qubits reside. The physical wave function can be represented by projecting a slater determinant for three layers to the physical layers with each site's ancilla qubits forming a local singlet.

Here we try to apply this method to a generic Hubbard model. We focus on the half filled case for now.  we use parameter Φ to represent the energy scale of charge gap. We rigorously prove that the variational wave function in the large Φ limit is the same state as the well-known Gutzwiller wave function.  We argue that finite Φ case is a good ansatz for weak Mott insulator for finite charge gap.  

We demonstrated this  for the spin-1/2 Hubbard model in one dimension. We show that the overlap between the ansatz (with single variational parameter Φ) and the realistic ground states is near 1 for the Hubbard model at site number equals to 8 for the whole range of U.   For two dimension, we argue that there may be an exotic pseudogap metal phase sandwiched between Fermi liquid and Mott insualtor.