Improved methods for demonstrating that AKLT systems are gapped

We examine recent advancements in proving the gaps of AKLT systems [1,2], in particular those proposed by Abdul-Rahman et al. [1], which we have later extended so that it can be applied numerically in more general settings. We discuss how this has been used in proving the AKLT gap on a variety of "decorated" lattices in 2D, where the number n of decorating spin-1 sites on each edge of the original lattice is two or larger [3]. Furthermore, we investigate whether the gappedness can be established for several decorated lattices with n=1. We will further explore how the method may be used to demonstrate the existence of the AKLT gap on several uniform lattices without decoration.

[1] H. Abdul-Rahman, M. Lemm, A. Lucia, B. Nachtergaele, and A. Young, arXiv:1901.09297
[2] M. Lemm, A. Sandvik, and S. Yang, arXiv:1904.01043.
[3] N. Pomata and T.-C. Wei, Phys. Rev. B 100, 094429 (2019)