Effective low-energy description of almost Ising-Heisenberg diamond chain

Abstract

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...

Fractional magnetization plateaus of the spin-12Heisenberg orthogonal-dimer chain: Strong-coupling approach developed from the exactly solved Ising-Heisenberg model

“…54 and references cited therein). Quite recently, the similar perturbation procedure starting from the exactly solved spin-1/2 Ising-Heisenberg diamond chain has been applied to corroborate an existence of the Tomonaga-Luttinger spin-liquid phase in between the intermediate one-third plateau and saturation magnetization of the quantum spin-1/2 Heisenberg diamond chain 55 . Our further goal is to apply the developed strong-coupling approach to To study the magnetization process and the groundstate phase diagram, we have to distinguish two cases: m ≤ m sat /2 and m ≥ m sat /2.…”

Magnetoelastic properties of a spin-1/2 Ising-Heisenberg diamond chain in vicinity of a triple coexistence point

“…Lately, different versions of the Ising-Heisenberg diamond chains have provided a useful playground full of intriguing features and unexpected findings such as the existence of intermediate magnetization plateaus [24][25][26], Lyapunov exponent and superstability [27], the non-conserved magnetization and "fire-and-ice" ground states [28], the enhanced magnetocaloric effect [29], the pseudo-critical behavior mimicking a temperature-driven phase transition [30][31][32][33] or the pseudo-universality [34]. Most importantly, Derzhko and co-workers [35] convincingly evidenced that the exact solution for the Ising-Heisenberg diamond chain may be used as a useful starting point for the perturbative treatment of the full Heisenberg counterpart model. It was shown that this type of many-body perturbation theory may even bring insight into exotic quantum states such as a quantum spin liquid not captured by the original Ising-Heisenberg model [35].…”

“…Most importantly, Derzhko and co-workers [35] convincingly evidenced that the exact solution for the Ising-Heisenberg diamond chain may be used as a useful starting point for the perturbative treatment of the full Heisenberg counterpart model. It was shown that this type of many-body perturbation theory may even bring insight into exotic quantum states such as a quantum spin liquid not captured by the original Ising-Heisenberg model [35].…”

Frustrated quantum Heisenberg double-tetrahedral and octahedral chains at high magnetic fields

“…Effects of small deviation from ideal flat-band geometry were studied in references [8][9][10][11][12][13] . In particular, to study high-field low-temperature properties of initial deformed one-or two-dimensional frustrated Heisenberg antiferromagnets effective Hamiltonians were constructed using the localized-magnon approach.…”