Single-hole wavefunction in two dimensions: A case study of the doped Mott insulator

We study a ground-state ansatz for the single hole doped t-J model in two dimensions via a
variational Monte Carlo method. Such a single hole wavefunction possesses a composite
structure with a fnite angular momentum associated with hidden spin currents, which gives rise to
a novel ground state degeneracy in agreement with recent ED and DMRG results.
We further show that the wavefunction is composed of a quasiparticle component and an incoherent momentum distribution in excellent agreement with the DMRG results up to an 8*8 lattice. But the quasiparticle spectral weight determined by
the VMC vanishes in a power-law fashion, indicating that the doped hole becomes a non-Landau
quasiparticle in the large sample-size limit. Here the bare hole propagator decays much faster
as compared to the composite hole over a spatial distance, supporting the picture that a bare
hole must be turned into a "twisted" quasiparticle in order to propagate more coherently in an
antiferromagnetic background. However, by turning on the phase string induced by the hole hopping
in the t-J model, a normal Bloch-wave wavefunction with a fnite quasiparticle spectral weight and
conventional quantum numbers can be simply recovered in the so-called \sigma t-J model, again well
agreeing with the ED and DMRG results.