Help Identifying Tree
It looks like this could be Lotebush, Ziziphus obtusifolia. The thorny branchlets and blue-green color (at least, as it appears in the photos) suggest Ziziphus to me, although you could compare it with the photos or description here. If it is in the buckthorn family, it does seem to key out to Ziziphus using the Christie et al. key.

If you wanted to be sure, you could follow up with the ASU herbarium (see citation).



Christie, K., M. Currie, L.S. Davis, M.-E. Hill, S. Neal and T. Ayers (2006). Vascular Plants of Arizona: Rhamnaceae. Canotia 2(1): 23-46. Open access