Spin systems with dimerized ground states

Abstract

In view of the numerous examples in the literature it is attempted to outline a theory of Heisenberg spin systems possessing dimerized ground states (``DGS systems") which comprises all known examples. Whereas classical DGS systems can be completely characterized, it was only possible to provide necessary or sufficient conditions for the quantum case. First, for all DGS systems the interaction between the dimers must be balanced in a certain sense. Moreover, one can identify four special classes of DGS systems: (i) Uniform pyramids, (ii) systems close to isolated dimer systems, (iii) classical DGS systems, and (iv), in the case of $s=1/2$, systems of two dimers satisfying four inequalities. Geometrically, the set of all DGS systems may be visualized as a convex cone in the linear space of all exchange constants. Hence one can generate new examples of DGS systems by positive linear combinations of examples from the above four classes.

With corrections of proposition 4 and other minor changes

References in corpus (7)

• Exact dimer ground state of the two dimensional Heisenberg spin system SrCu_2(BO_3)_2
• Macroscopic entanglement jumps in model spin systems
• Competition between plaquette and dimer phases in Heisenberg chains
• The antiferromagnetic spin 1/2 chain with competing dimers and plaquettes: Numerical versus exact results
• Quantum spin models with exact dimer ground states
• Linear energy bounds for Heisenberg spin systems
• Generalised Shastry-Sutherland Models in three and higher dimensions

Cited by in corpus (9)

• Emergent Ising degrees of freedom in frustrated two-leg ladder and bilayer $s=1/2$ Heisenberg antiferromagnets
• Quantum phase transitions in the exactly solved spin-1/2 Heisenberg-Ising ladder
• Ground-state phase diagram of the spin-1/2 square-lattice J1-J2 model with plaquette structure
• Exact ground states for coupled spin trimers
• Generalized mean field description of entanglement in dimerized spin systems
• Exact ground states of frustrated quantum spin systems consisting of spin-dimer units
• Pair entanglement in dimerized spin-s chains
• Triplon mean-field analysis of an antiferromagnet with degenerate Shastry-Sutherland ground states
• Covariance-based method for eigenstate factorization and generalized singlets