The spin-orbital model for triply degenerate
t2g electrons on a triangular lattice has been shown to be dominated by dimers. The phase diagram contains both strongly resonating, compound spin-orbital dimer states and quasistatic, spin-singlet valence-bond (VB) states. To elucidate the nature of the true ground state in these different regimes, the model is mapped to a number of quantum dimer models (QDMs), each of which has three dimer colors. The generic multicolored QDM, illustrated for the two- and three-color cases, possesses a topological color structure, ``color vison'' excitations, and broad regions of resonating VB phases. The specific models are analyzed to gain further insight into the likely ground states in the superexchange and direct-exchange limits of the electronic Hamiltonian, and they suggest a strong tendency toward VB order in all cases.
Using Lanczos exact diagonalization (ED), we study the spin-1/2 ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model with the four-spin ring-exchange interaction
Jr on a triangular lattice. We mainly use the level spectroscopic technique of two 36-site tori to investigate the ground-state phase diagram, and further characterize phases by spin, dimer, and chiral correlation functions. The ground state has rich phases including several magnetic-ordered phases like the zigzag phase and tetrahedral phase, as well as several novel nonmagnetic phases, some of which exhibit valence bond solid behavior in their dimer correlation functions. However, we do not find direct evidence of a quantum spin liquid phase with spinon Fermi surface in this model. Our results can give a better understanding of the ground-state properties of the triangular Heisenberg model with ring-exchange interaction and help to understand the relevant triangular materials.
We performed an exact diagonalization study of the spin-liquid phase of the multiple-spin exchange model on a triangular lattice. It is characterized by no N\'eel long-range order, short-ranged magnetic correlations, and a spin gap. We found no long-range order in any local order parameter we investigated (chiral, dimer, etc.) The probable asymptotic ground-state degeneracy is discussed. We argue that it could be of topological origin and that the system is probably not a chiral spin liquid. A possible relation to the Affleck-Kennedy-Lieb-Tasaki, or valence-bond solid phase is discussed.
Ideas about resonant valence bond liquids and spin-charge separation have led to key concepts in physics such as quantum spin liquids, emergent gauge symmetries, topological order and fractionalization. Despite extensive efforts to demonstrate the existence of a resonant valence bond phase in the Hubbard model that originally motivated the concept, a definitive realization has yet to be achieved. Here we present a solution to this long-standing problem by uncovering a resonant valence bond phase exhibiting spin-charge separation in realistic Hamiltonians. We show analytically that this ground state emerges in the dilute-doping limit of a half-filled Mott insulator on corner-sharing tetrahedral lattices with frustrated hopping, in the absence of exchange interactions. We confirm numerically that the results extend to finite exchange interactions, finite-sized systems and finite dopant density. Although much attention has been devoted to the emergence of unconventional states from geometrically frustrated interactions, our work demonstrates that kinetic energy frustration in doped Mott insulators may be essential for stabilizing robust, topologically ordered states in real materials.
We study the half-filled single-band Hubbard model on the Shastry–Sutherland lattice with nearest-neighbor hopping
t, incorporating (i) a frustrating diagonal hopping
t′ to probe the emergence of spin-liquid behavior, and (ii) an additional Heisenberg exchange
J that explicitly stabilizes plaquette-singlet correlations. Using the variational cluster approximation (VCA) with exact diagonalization at zero temperature on an eight-site cluster, we map the phase diagrams in the
(U/t,t′/t) and
(U/t,J/t) parameter planes. In the
(U/t,t′/t) plane, our analysis uncovers a competition between N\'eel antiferromagnetic (AFM) order with staggered magnetization and a nonmagnetic regime lacking conventional order, consistent with an algebraic spin-liquid (ASL) phase characterized by a gapped excitation spectrum and vanishing staggered magnetization. In contrast, the
(U/t,J/t) phase diagram exhibits a competition between the N\'eel AFM and a solid valence-bonding valence bond plaquette (PS), where spins form localized singlet plaquettes. Most notably, we observe that the transition from the PS phase to the N\'eel AFM is a first-order phase transition, with a discontinuous jump of the order parameters at the phase boundary, in quantitative agreement with high-pressure heat-capacity measurements on SrCu
2(BO
3)
2 [Guo \emph{et al.}, Commun. Phys. 8, 75 (2025)]. Thus, our VCA analysis underscores the subtle interplay of geometric frustration, quantum fluctuations, and dimensionality, and elucidates the crucial role of short-range correlations in stabilizing and competing ground states of frustrated quantum magnets.