Numerical Study of Bond-Nematic Order in Spin S=1/2 Frustrated Ferromagnets on the Square Lattice

In the absence of conventional magnetic order of spin-dipolar moments, ordering with higher-order moments like spin-quadrupoles may occur. Magnets with spin-1/2 degrees of freedom, however, can only exhibit spin-quadrupoles---or spin-nematic states---if two spin-1/2 are combined into an effective spin-1. Such bond-nematic phase has theoretically been observed in frustrated ferromagnets on the square lattice [Shannon2006]. Motivated by recent experiments suggesting the existence of spin-nematic order in volborthite in applied magnetic field [Kohama2019], we revisit the square-lattice frustrated ferromagnets using a combination of modern numerical techniques, namely matrix-product states based methods and high-field exact diagonalization. We confirm the existence of the bond-nematic phase sandwiched between the fully-polarized phase at high fields and a long-range magnetically ordered phase at low fields, and characterise its microscopic properties. These methods enable us to study its dynamical fingerprint---a characteristic Goldstone mode associated with the director of the spin-quadrupole---taking into account the strongly interacting many-body nature in a controlled way.