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arXiv:0909.2182

Spin models of quasi-1D quantum ferrimagnets with competing interactions

Nedko B. Ivanov

Published Sep 11, 2009• 3 citations
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Abstract

We present a brief survey of the recent theoretical work related to generic Heisenberg spin models describing quasi-one-dimensional quantum ferrimagnets. The emphasis is on quantum chains and ladders with strong competing interactions, such as the frustrated $J_1-J_2$ chain with alternating (1,1/2) spins, the spin-1/2 diamond chain with four-spin cyclic couplings, and some generic types of mixed-spin ladders with geometric frustration. As a rule, discussed models exhibit rich quantum phase diagrams and provide some interesting examples of one-dimensional magnetic-paramagnetic quantum phase transitions. A number of open problems in the reviewed research area are discussed.

DOI
10.48550/arxiv.0909.2182

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We present a brief survey of the recent theoretical work related to generic Heisenberg spin models describing quasi-one-dimensional quantum ferrimagnets. The emphasis is on quantum chains and ladders with strong competing interactions, such as the frustrated J1−J2J_1-J_2J1​−J2​ chain with alternating (1,1/2) spins, the spin-1/2 diamond chain with four-spin cyclic couplings, and some generic types of mixed-spin ladders with geometric frustration. As a rule, discussed models exhibit rich quantum phase diagrams and provide some interesting examples of one-dimensional magnetic-paramagnetic quantum phase transitions. A number of open problems in the reviewed research area are discussed.
We present a brief survey of the recent theoretical work related to generic Heisenberg spin models describing quasi-one-dimensional quantum ferrimagnets.The emphasis is on quantum chains and ladders with strong competing interactions, such as the frustrated J 1 -J 2 chain with alternating (1, 1/2) spins, the spin-1/2 diamond chain with four-spin cyclic couplings, and some generic types of mixed-spin ladders with geometric frustration.As a rule, the discussed models exhibit rich quantum phase diagrams and provide some interesting examples of one-dimensional magnetic-paramagnetic quantum phase transitions.A number of open problems in the reviewed research area are discussed.
We study the impact of the diagonal frustrating couplings on the quantum phase diagram of a two-leg ladder composed of alternating spin-1 and spin-12\frac{1}{2}21​ rungs. As the coupling strength is increased the system successively exhibits two gapped paramagnetic phases (a rung-singlet and a Haldane-type nondegenerate states) and two ferrimagnetic phases with different ferromagnetic moments per rung. The first two states are similar to the phases studied in the frustrated spin-12\frac{1}{2}21​ ladder, whereas the magnetic phases appear as a result of the mixed-spin structure of the model. A detailed characterization of these phases is presented using density-matrix renormalization-group calculations, exact diagonalizations of periodic clusters, and an effective Hamiltonian approach inspired by the analysis of numerical data. The present theoretical study was motivated by the recent synthesis of the quasi-one-dimensional ferrimagnetic material FeIIFeIII{\text{Fe}}^{\text{II}}{\text{Fe}}^{\text{III}}FeIIFeIII (trans-1,4-cyclohexanedicarboxylate) exhibiting a similar ladder structure.
We study the magnetic phase diagram of two coupled mixed-spin (1,12)(1,\frac{1}{2})(1,21​) Heisenberg chains as a function of the frustration parameter related to diagonal exchange couplings. The analysis is performed by using spin-wave series and exact numerical diagonalization techniques. The obtained phase diagram---containing the Luttinger liquid phase, the plateau phase with a magnetization per rung M=1∕2M=1∕2M=1∕2, and the fully polarized phase---is closely related to the generic $(J∕U,\ensuremath{\mu}∕U)$ phase diagram of the one-dimensional boson Hubbard model.
We study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic (J1FJ_1^FJ1F​) and antiferromagnetic (J1AJ_1^AJ1A​) nearest-neighbor interactions and ferromagnetic next-nearest-neighbor interaction (J2FJ_2^FJ2F​). In this model frustration is induced by the non-zero J2FJ_2^FJ2F​ and the effect of dimerization is realized by changing the strength of J1AJ_1^AJ1A​ for a fixed value of J1FJ_1^FJ1F​. The model with site spin sss behaves like a Haldane spin chain with site spin 2sss in the limit of vanishing J2FJ_2^FJ2F​ and large J1F/J1AJ_1^F/J_1^AJ1F​/J1A​. We show that the exact ground state of the model can be found along a line in the parameter space. The phase diagram in the space of J1A−J2FJ_1^A-J_2^FJ1A​−J2F​ is determined using numerical techniques complemented by some analytical calculations. A number of quantities, including the ground state spin, energy gap, structure factor, entanglement entropy, and zero temperature magnetization, are studied to understand the complete phase diagram. An interesting and application-wise important feature of this model is that it exhibits a macroscopic magnetization jump in the presence of a magnetic field; we study this using an effective Hamiltonian.
In this topical review, we explore low-dimensional spin-12\frac{1}{2}21​ systems, focusing on key models such as the Majumdar-Ghosh (MG) model on a spin-12\frac{1}{2}21​ chain and the Heisenberg spin-12\frac{1}{2}21​ model applied to various ladder geometries, including normal, zigzag, two-leg honeycomb, skewed, and diamond. We discuss the key physical features and experimental realizations of these models in real materials, providing a detailed overview. The review also includes the Kitaev-Heisenberg model on a two-leg ladder, a recent development in quantum magnetism. It discusses emerging quantum phases, such as spin liquids and magnetization plateaus, and highlights open research areas, including the investigation of unexplored exotic ground states. Additionally, we briefly discuss how quantum simulators based on ion traps, superconducting circuits, optical lattices, etc., are being used as powerful tools to explore the ground-state phases of spin-12\frac{1}{2}21​ systems. Furthermore, the review emphasizes the potential for new material design, offering an exciting avenue for future experimental and theoretical advancements in low-dimensional quantum systems.
We present the ground-state phase diagram of q=1/2q=1/2q=1/2 quantum-rotor chains with competing interactions (frustration) calculated through cluster variational mean field approaches. We consider two interaction patterns, named F1{\text{F}}_{1}F1​ and F2{\text{F}}_{2}F2​ models, between the quantum-rotor momentum and position operators, which follow exchange patterns of known one-dimensional spin-1/2 systems with a ferrimagnetic state in their phase diagrams. The spin-1/2 F1{\text{F}}_{1}F1​ model is known as the diamond chain and is related to the azurite compound, while the spin-1/2 F2{\text{F}}_{2}F2​ model was recently shown to present a frustration-induced condensation of magnons. We provide a detailed comparison between the quantum-rotor phase diagrams, in single- and multisite mean-field approaches, and known results for the spin-1/2 models, including exact diagonalization and density matrix renormalization group data for these systems, as well as phase diagrams of the associated classical models.