They study my favourite Hubbard model: the half-filled model on an anisotropic triangular lattice, within a new approximation scheme.
Basically, they start with a functional integral representation and ignore the dynamical fluctuations in the local magnetisation. One is then left with calculated the electronic spectrum for an inhomogeneous spin distribution and averaging then averaging over these with the relevant Boltzmann weights. This has the significant computational/technical advantage that the calculation is a classical Monte Carlo simulation.
Hence, it treats spatial spin fluctuations exactly while neglecting dynamical fluctuations.
This is a nice study because it complements the approximation of dynamical mean-theory (DMFT): it ignores spatial fluctuations but treats dynamical fluctuations exactly.
The calculation captures some of the important properties of the model: the Mott transition, a bad metal, and a possible pseudogap phase.
This shows how an anisotropic pseudogap can arise in the model due to short-range antiferromagnetic spin fluctuations (clearly shown in Figure 5 of the paper, reproduced below).
However, as I would expect, this approximation cannot capture some of the key physics that DMFT does: the co-existence of Hubbard bands and a Fermi liquid. This difference is clearly seen in the optical conductivity calculated by the two different methods.
There must be some connection with old studies [motivated by the cuprates] of Schmalian, Pines, and Stojkovic, of electrons coupled to static spin fluctuations with finite-range correlations [see e.g. this PRB].
This combined importance of both dynamical and spatial fluctuations highlights to me the importance of a recent study by Jure Kokalj and I, which treated them on the same footing by using the finite temperature Lanczos method on small lattices.