Candidate Clusters of Galaxies at $z>1.3$ Identified in the Spitzer SPT
  Deep Field Survey
  We present 279 galaxy cluster candidates at $z > 1.3$ selected from the 94
deg$^{2}$ Spitzer South Pole Telescope Deep Field (SSDF) survey. We use a
simple algorithm to select candidate high-redshift clusters of galaxies based
on Spitzer/IRAC mid-infrared data combined with shallow all-sky optical data.
We identify distant cluster candidates in SSDF adopting an overdensity
threshold that results in a high purity (80%) cluster sample based on tests in
the Spitzer Deep, Wide-Field Survey of the Bo\"otes field. Our simple algorithm
detects all three $1.4 < z \leq 1.75$ X-ray detected clusters in the Bo\"otes
field. The uniqueness of the SSDF survey resides not just in its area, one of
the largest contiguous extragalactic fields observed with Spitzer, but also in
its deep, multi-wavelength coverage by the South Pole Telescope (SPT),
Herschel/SPIRE and XMM-Newton. This rich dataset will allow direct or stacked
measurements of Sunyaev-Zel'dovich effect decrements or X-ray masses for many
of the SSDF clusters presented here, and enable systematic study of the most
distant clusters on an unprecedented scale. We measure the angular correlation
function of our sample and find that these candidates show strong clustering.
Employing the COSMOS/UltraVista photometric catalog in order to infer the
redshift distribution of our cluster selection, we find that these clusters
have a comoving number density $n_c = (0.7^{+6.3}_{-0.6}) \times 10^{-7} h^{3}
\mathrm{Mpc}^{-3}$ and a spatial clustering correlation scale length $r_0 = (32
\pm 7) h^{-1} \rm{Mpc}$. Assuming our sample is comprised of dark matter halos
above a characteristic minimum mass, $M_{{\rm min}}$, we derive that at $z=1.5$
these clusters reside in halos larger than $M_{{\rm min}} = 1.5^{+0.9}_{-0.7}
\times 10^{14} h^{-1} M_{\odot}$. (abridged)
