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10.58160/r3vnr5repv8syuq1 Schwab, Jonas Jonas Schwab 0000-0003-3794-8631 University of Würzburg University of Würzburg 2023 2024 Physics Quantum Monte Carlo Antiferromagnetism Quantum Spin Models Phase diagrams Heisenberg model SU(N) symmetries Topological phases of matter Open Access Creative Commons Attribution 4.0 International Schwab, Jonas 0000-0003-3794-8631 Assaad, Fakher F. 0000-0002-3302-9243 Assaad, Fakher Fakhry 0000-0002-3302-9243 University of Würzburg Parisen Toldin, Francesco 0000-0002-1884-9067 RWTH Aachen University 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 en 10.1103/PhysRevB.108.115151 10.48550/arXiv.2304.07329 Deutsche Forschungsgemeinschaft https://ror.org/018mejw64 258499086 SFB 1170: Topologische und korrelierte Elektronik in Ober- und Grenzflächen ("ToCoTronics") Complexity and Topology in Quantum Matter https://ror.org/00kkpv737 390858490 EXC 2147: Komplexität und Topologie in Quantenmaterialien (CT.QMAT) Deutsche Forschungsgemeinschaft https://ror.org/018mejw64 414456783 Kritische Phänomene im Bulk und auf dem Rand von verallgemeinerten Quantenantiferromagneten application/x-tar