Exact solution of the geometrically frustrated spin-1/2 Ising-Heisenberg model on the triangulated Kagome (triangles-in-triangles) lattice

TL;DR

This paper provides an exact analytical solution for the spin-1/2 Ising-Heisenberg model on a triangulated Kagome lattice, revealing how quantum fluctuations influence ground-state degeneracy and phase behavior in a frustrated magnetic system.

Contribution

It introduces an exact solution method for the model using star-triangle mapping, connecting it to the Kagome Ising model, and analyzes quantum effects on residual entropy and phase diagrams.

Findings

Quantum fluctuations reduce residual entropy compared to classical limit.

Exact phase diagrams and thermodynamic quantities are obtained.

Predictions made for specific heat behavior in related compounds.

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 is for the quantum Ising-Heisenberg model significantly lower than for its semi-classical 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 Cu_9X_2(cpa)_6 (X=F, Cl, Br and cpa=carboxypentonic acid) for which we made a theoretical prediction about the temperature dependence of zero-field specific heat.