Data to reproduce the results of the publication: Jonas Schwab, Francesco Parisen Toldin, and Fakher F. Assaad. "Phase diagram of the SU(𝑁) antiferromagnet of spin 𝑆 on a square lattice" Phys. Rev. B, 108:115151, Sep 2023. arXiv:2304.07329, doi:10.1103/PhysRevB.108.115151.

Paper 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 four-fold degenerate valence bond solid phase. In the large $S$-limit, the semi-classical approximation points to 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 four fold degenerate valence bond solid state. At $S=1$ a two fold degenerate spin nematic state in which the C$_4$ lattice symmetry is broken down to C$_2$ 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).

Please read the 'README' file.

This research has been funded by the Deutsche Forschungsgemeinschaft (DFG) through the Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter ct.qmat (EXC 2147, Project No. 390858490), the SFB1170 on Topological and Correlated Electronics at Surfaces and Interfaces (Project No. 258499086), Project No. 414456783 and Grant No. AS 120/14-1. The authors gratefully acknowledge the Gauss Centre for Supercomputing e.V. for funding this project by providing computing time on the GCS Supercomputer SuperMUC-NG at Leibniz Supercomputing Centre. The authors gratefully acknowledge the scientific support and HPC resources provided by the Erlangen National High Performance Computing Center (NHR@FAU) of the Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) under the NHR project b133ae. NHR funding is provided by federal and Bavarian state authorities. NHR@FAU hardware is partially funded by the German Research Foundation (DFG) – 440719683.

The data has been produced through Quantum Monte Carlo simulations with Algorthims for Lattice Fermions (ALF, https://doi.org/10.21468/SciPostPhysCodeb.1), using the Hamiltonian documented in here: https://gitpages.physik.uni-wuerzburg.de/alf/hamiltonians/Hamiltonians/AFM_N_S/README.html