Phase diagram of the SU($N$) antiferromagnet of spin $S$ on a square lattice

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 $\text{mod}(4,2S)$.

18 pages, 21 figures; adapted title to APS style and included minor corrections

References in corpus (10)

• "Deconfined" quantum critical points
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Fermionic quantum criticality in honeycomb and $\pi$-flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo
• Spin-orbital quantum liquid on the honeycomb lattice
• Spin--orbital interaction for face-sharing octahedra: Realization of a highly symmetric SU(4) model
• Phases of the (2+1) dimensional SO(5) non-linear sigma model with topological term
• SU(N) quantum spin models: A variational wavefunction study
• Critical behavior in the presence of an order-parameter pinning field
• Finite Temperature Auxiliary Field Quantum Monte Carlo in the Canonical Ensemble
• Finite-size effects in canonical and grand-canonical quantum Monte Carlo simulations for fermions

Cited by in corpus (2)

• Alteration of Topology in Quantum Phase Transitions via Symmetry Enrichment
• Phases and phase transitions of an $S=3/2$ chain on metallic and semi-metallic surfaces