We consider a geometrically frustrated spin-1/2 Ising-Heisenberg diamond chain, which is an exactly solvable model when assuming part of the exchange interactions as Heisenberg ones and another part as Ising ones. A small XY part is afterwards perturbatively added to the Ising couplings, which enabled us to derive an effective Hamiltonian describing the low-energy behavior of the modified but full quantum version of the initial model. The effective model is much simpler and free of frustration. It is shown that the XY part added to the originally Ising interaction gives rise to the spin-liquid phase with continuously varying magnetization, which emerges in between the magnetization plateaus and is totally absent in the initial hybrid diamond-chain model. The elaborated approach can also be applied to other hybrid Ising-Heisenberg spin systems. Exactly solvable models, which can be solved without resorting to approximations, are of great importance in statistical mechanics and condensed matter physics since they provide milestones for our understanding of macroscopic properties of matter.1,2 Well-known examples of such models are Ising models, vertex models, Betheansatz models, etc. Nowadays, numerous variations of Kitaev model 3 become quite popular. Another way how to get exactly solvable models is to consider the so-called hybrid classical-quantum models, which can be viewed as a regular pattern of small quantum parts linked through classical parts. After making some transformations they can be mapped onto a simpler fully classical models with known exact solutions.
4-7One illustrating example of such a hybrid classicalquantum model is an Ising-Heisenberg diamond chain, see Fig. 1. This model takes into account the Heisenberg interaction J along the vertical bonds and the Ising interaction I along the bonds forming diamond motifs. In other words, the quantum Heisenberg spins (s-spins) are situated at the bottom and top sites (k, 1 and k, 2) of the vertical bonds and the Ising spins (µ-spins) are placed at the connecting interstitial sites k, k = 1, . . . , N , and N = 3N is the total number of sites in the diamond chain, see Fig. 1. Over the last two decades, various versions of the spin-1/2 Heisenberg diamond chain have been extensively studied within different approaches.
8,9The considerable interest aimed at this model has been stimulated by several solid-state realizations of the spin-1/2 Heisenberg diamond chain.10,11 It is noteworthy that the simplified Ising-Heisenberg diamond-chain model allows a complete rigorous solution for all equilibrium properties.
12-15Although hybrid models can be also found among solidstate systems, 16 it seems more plausible to find in real life a case around the exactly solvable point. In the present study we will therefore address a question how to describe almost hybrid classical-quantum spin models, in which the Ising couplings acquire a small XY part. The developed approach will be illustrated on a particular example of the frustrated spin-1/2 diamond-chain model, for wh...