Exact solution of the geometrically frustrated spin-12Ising-Heisenberg model on the triangulated kagome (triangles-in-triangles) lattice

Abstract

The geometric frustration of the spin-1/2 Ising-Heisenberg model on the triangulated kagome (triangles-in-triangles) lattice is investigated within the framework of an exact analytical method based on the generalized star-triangle mapping transformation. Ground-state and finite-temperature phase diagrams are obtained along with other exact results for the partition function, Helmholtz free energy, internal energy, entropy, and specific heat, by establishing a precise mapping relationship to the corresponding spin-1/2 Ising model on the kagome lattice. It is shown that the residual entropy of the disordered spin liquid phase for the quantum Ising-Heisenberg model is significantly lower than for its semiclassical Ising limit (${S}_{0}/{N}_{T}{k}_{B}=0.2806$ and 0.4752, respectively), which implies that quantum fluctuations partially lift a macroscopic degeneracy of the ground-state manifold in the frustrated regime. The investigated model system has an obvious relevance to a series of polymeric coordination compounds ${\text{Cu}}_{9}{X}_{2}{(\text{cpa})}_{6}$ ($X=\text{F}$,Cl,Br and $\text{cpa}=\text{carboxypentonic}$ acid), for which we made a theoretical prediction about the temperature dependence of zero-field specific heat.