Article,
Phase diagram of the SU(N) antiferromagnet of spin S on a square lattice
Phys. Rev. B, 108 (11): 115151 (Sep 25, 2023)
DOI: 10.1103/PhysRevB.108.115151
Abstract
We investigate the ground-state phase diagram of an SU(N)-symmetric antiferromagnetic spin model on a square lattice where each site hosts an irreducible representation of SU(N) described by a square Young tableau of N/2 rows and 2S columns. We show that negative sign free fermion Monte Carlo simulations can be carried out for this class of quantum magnets at any S and even values of N. In the large-N limit, the saddle point approximation favors a fourfold degenerate valence bond solid phase. In the large S limit, the semiclassical approximation points to the Néel state. On a line set by N=8S+2 in the S versus N phase diagram, we observe a variety of phases proximate to the Néel state. At S=1/2 and 3/2, we observe the aforementioned fourfold degenerate valence bond solid state. At S=1, a twofold degenerate spin nematic state in which the C4 lattice symmetry is broken down to C2 emerges. Finally, at S=2 we observe a unique ground state that pertains to a two-dimensional version of the Affleck-Kennedy-Lieb-Tasaki state. For our specific realization, this symmetry-protected topological state is characterized by an SU(18), S=1/2 boundary state that has a dimerized ground state. These phases that are proximate to the Néel state are consistent with the notion of monopole condensation of the antiferromagnetic order parameter. In particular, one expects spin-disordered states with degeneracy set by mod(4,2S).
