Adjoint ferromagnets

Abstract

We derive the phase structure and thermodynamics of ferromagnets consisting of elementary magnets carrying the adjoint representation of $SU(N)$ and coupled through two-body quadratic interactions. Such systems have a continuous $SU(N)$ symmetry as well as a discrete conjugation symmetry. We uncover a rich spectrum of phases and transitions, involving a paramagnetic and two distinct ferromagnetic phases that can coexist as stable and metastable states in different combinations over a range of temperatures. The ferromagnetic phases break $SU(N)$ invariance in various channels, leading to spontaneous magnetization. Interestingly, the conjugation symmetry also breaks over a range of temperatures and group ranks $N$, providing a realization of a spontaneously broken discrete symmetry.

31 pages, 8 figures

References in corpus (18)

• Spectroscopic observation of SU(N)-symmetric interactions in Sr orbital magnetism
• Ultracold Gases of Ytterbium: Ferromagnetism and Mott States in an SU(6) Fermi System
• Itinerant Ferromagnetism in an Ultracold Atom Fermi Gas
• Phases of one-dimensional SU(N) cold atomic Fermi gases --from molecular Luttinger liquids to topological phases
• Exact Spectrum of SU(n) Spin Chain with Inverse-Square Exchange
• Quantum and Thermal Phase Transitions of the Triangular SU(3) Heisenberg Model under Magnetic Fields
• Nagaoka states in the SU($n$) Hubbard model
• Chiral Haldane phases of SU(N) quantum spin chains in the adjoint representation
• Semi-classical simulation of spin-1 magnets
• Structure of Spin Correlations in High Temperature SU($N$) Quantum Magnets
• Ferromagnetism in $d$-dimensional SU($n$) Hubbard models with nearly flat bands
• Semiclassical Approach to Competing Orders in Two-leg Spin Ladder with Ring-Exchange
• Symmetry-protected topological phases in two-leg SU(N) spin ladder with unequal spins
• Composition of many spins, random walks and statistics
• Ferromagnetism in the SU(N) Kondo lattice model -- SU(N) double exchange and supersymmetry
• Composing arbitrarily many $SU(N)$ fundamentals
• Phase transitions in the decomposition of $SU(N)$ representations
• Nonabelian ferromagnets with three-body interactions