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 Kagomé (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 Kagomé 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 (S0/NTkB = 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 Cu9X2(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.

Presence or absence of order by disorder in a highly frustrated region of the spin-1/2 Ising-Heisenberg model on triangulated Husimi lattices

“…It is worth mentioning that the overall ground-state eigenvector is given by a tensor product over the lowestenergy eigenstates of the cluster Hamiltonians (3), which means that the ground-state phase diagram and individual ground states of the spin-1/2 Ising-Heisenberg model on triangulated Husimi lattices are completely identical with that reported on previously for the analogous model on triangulated planar lattices composed of the same structural unit [29][30][31]. In this regard, let us merely quote individual ground-state eigenvectors of the spin-1/2 Ising-Heisenberg model on triangulated Husimi lattices without their detailed description (the interested reader is referred to Ref.…”

“…It has been convincingly evidenced [31] that the spin-1/2 Ising-Heisenberg model with a greater connectivity of triangles-in-triangles units in the underlying triangular lattice gives rise to stronger local quantum fluctuations, which preferably support a remarkable quantum order at low enough temperatures instead of a quantum disorder through the order-by-disorder effect. Contrary to this, the spin-1/2 Ising-Heisenberg model on triangulated kagomé lattice cannot exhibit this intriguing feature [29,30]. Bearing this in mind, it appears worthwhile to examine the spin-1/2 Ising-Heisenberg model on related triangulated Husimi lattices, in which the connectivity of triangles-in-triangles units can be varied systematically.…”

“…Recently, the spin-1/2 Ising-Heisenberg model on triangulated (triangles-in-triangles) planar lattices have attracted a great deal of attention [29][30][31][32], because it closely resembles a magnetic structure of real polymeric coordination compounds Cu 9 X 2 (cpa) 6 ·nH 2 O (X=F,Cl,Br) with the geometry of triangulated kagomé lattice [26][27][28]. Besides a clear experimental motivation, the spin-1/2 Ising-Heisenberg model on triangulated planar lattices has afforded a valuable playground for an investigation of the role of local quantum fluctuations within a novel class of exactly solvable classical-quantum spin systems.…”

The Heisenberg antiferromagnet on the square-kagomé lattice

“…These studies are motivated by the recent progress in synthesizing quasi-two-dimensional magnetic materials which exhibit exciting quantum effects [3][4][5][6][7][8][9][10]. Even spin systems on more exotic frustrated lattices such as the star lattice [11,12], the maple-leaf lattice [13,11] and the triangulated kagomé lattice [14] have been synthesized recently [15][16][17].…”

A Consistent Description of Magnetic Properties of the Triangulated-Kagome System Cu9X2(cpa)6·nH2O

“…14, the ''minimum'' in T as observed experimentally has been reproduced, but the obtained magnetization reveals only the 5/9-plateau in the straightforward calculation, without taking into account the non-collinear spin arrangement of trimeric units resulting the 1/3-plateau. The thermodynamics of the Ising model, 16,17) Ising-Heisenberg mixed model, 15,[18][19][20] and Heisenberg model 21) have also been investigated; however, no consensus has not been arrived at even in the sign of the intertrimer exchange constant J AB , 22) because a consistent description of the increment in the gradient of À1 at low temperatures, of the existence of a ''minimum'' in T , and of the appearance of 1/3-plateau has not been successfully given.…”