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arXiv:2405.14378 · Physical Review Research

Spin- S Kitaev-Heisenberg model on the honeycomb lattice: A high-order treatment via the many-body coupled cluster method

M. Georgiou, Ioannis Rousochatzakis, DAMIAN J. J. FARNELL, Johannes Richter, R. F. Bishop

Published Aug 13, 2024• 14 citations
arXivHTMLPDF

Abstract

We study the spin- S Kitaev-Heisenberg model on the honeycomb lattice for S = 1 / 2 , 1, and 3 / 2 , by using the coupled cluster method (CCM) of microscopic quantum many-body theory. This system is one of the earliest extensions of the Kitaev model and is believed to contain two extended spin liquid phases for any value of the spin quantum number S . We show that the CCM delivers accurate estimates for the phase boundaries of these spin liquid phases, as well as other transition points in the phase diagram. Moreover, we find evidence of two unexpected narrow phases for S = 1 / 2 , one sandwiched between the zigzag and ferromagnetic phases and the other between the Néel and the stripy phases. The results establish the CCM as a versatile numerical technique that can capture the strong quantum-mechanical fluctuations that are inherently present in generalized Kitaev models with competing bond-dependent anisotropies. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.033168

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We explore the phase diagram of the Kitaev-Heisenberg model with nearest neighbor interactions on the honeycomb lattice using the exact diagonalization of finite systems combined with the cluster mean field approximation, and supplemented by the insights from analytic approaches: the linear spin-wave and second-order perturbation theories. This study confirms that by varying the balance between the Heisenberg and Kitaev term, frustrated exchange interactions stabilize in this model either one of four phases with magnetic long range order: N\'eel phase, ferromagnetic phase, and two other phases with coexisting antiferromagnetic and ferromagnetic bonds, zigzag and stripy phase, or one of two distinct spin-liquid phases. Out of these latter disordered phases, the one with ferromagnetic Kitaev interactions has a substantially broader range of stability as the neighboring competing ordered phases, ferromagnetic and stripy, have very weak quantum fluctuations. Focusing on the quantum spin-liquid phases, we study spatial spin correlations and dynamic spin structure factor of the model by the exact diagonalization technique, and discuss the evolution of gapped low-energy spin response across the quantum phase transitions between the disordered spin liquid and phases with long range magnetic order.
The coupled cluster method (CCM) of microscopic quantum many-body theory has become an ab initio method of first choice in quantum chemistry and many fields of nuclear, subnuclear and condensed matter physics, when results of high accuracy are required. In recent years it has begun to be applied with equal success to strongly correlated systems of electrons or quantum spins defined on a regular spatial lattice. One regularly finds that the CCM is able to describe accurately the various zero-temperature phases and the quantum phase transitions between them, even when frustration is present and other methods such as quantum Monte Carlo often fail. We illustrate the use and powerfulness of the method here by applying it to a square-lattice spin-half Heisenberg model where frustration is introduced by competing nearest neighbour bonds. The model exhibits the physically interesting phenomenon of competition between magnetic order and dimerization. Results obtained for the model with the CCM are compared with those found from spin-wave theory and from extrapolating the results of exact diagonalizations of small lattices. We show that the CCM is essentially unique among available methods in being able both to describe accurately all phases of this complex model and to provide accurate predictions of the various phase boundaries and the order of the corresponding transitions.
We study the ground-state phase diagram of the spin-1/21/21/2 Kitaev-Heisenberg model on the bilayer honeycomb lattice with large-scale tensor network calculations based on the infinite projected entangled pair state technique as well as high-order series expansions. We find that beyond various magnetically ordered phases, including ferromagnetic, zigzag, antiferromagnetic (AFM) and stripy states, two extended quantum spin liquid phases arise in the proximity of the Kitaev limit. While these ordered phases also appear in the monolayer Kitaev-Heisenberg model, our results further show that a valence bond solid state emerges in a relatively narrow range of parameter space between the AFM and stripy phases, which can be adiabatically connected to isolated Heisenberg dimers. Our results highlight the importance of considering interlayer interactions on the emergence of novel quantum phases in the bilayer Kitaev materials.
We study a spin model on honeycomb lattice with two types of Heisenberg exchange couplings, JJJ and $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{J}$, where JJJ is for the conventional spin and $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{J}$ is for rotated spin. When J=0J=0J=0, the system is either in a stripy antiferromagnetic order ($\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{J}<0$, ferromagnetic for rotated spin) or a zigzag antiferromagnetic order ($\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{J}>0$, antiferromagnetic for rotated spin). The competition between two ferromagnetic orders or between two antiferromagnetic orders induces Kitaev's spin liquid phase, characterized by the exactly solvable Kitaev model ($J=\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{J}$). Our model can be applied to layered Mott insulators AAA2{}_{2}2​IrO3{}_{3}3​ (A=LiA=\text{Li}A=Li, Na). For a monolayer of Li2{}_{2}2​IrO3{}_{3}3​, we show that it is possible to tune the controlling parameter into the Kitaev spin liquid regime by a link-dependent Rashba spin-orbital coupling.
Quantum spins arranged on regular geometrical lattices, and interacting through a wide diversity of specified model Hamiltonians, provide a rich variety of magnetically ordered phases with many subtle properties. The zero-temperature quantum phase transitions between states of different order can be explored by the variation of internal control parameters within the interaction Hamiltonian. We illustrate how the systematic inclusion of multi-spin correlations for such lattice systems may be efficiently and effectively implemented via the coupled cluster method (CCM), which has been widely demonstrated on many previous occasions to be one of the most versatile methods of microscopic quantum many-body theory. Its power is illustrated by application to the spin-½ anisotropic Heisenberg (or XXZ) model on an infinite square lattice. The results obtained for such properties as the ground-state energy and sublattice magnetization are found to be as accurate as those obtained by any available alternative method. We show also how the CCM can now provide accurate ab initio estimates for the critical values of the parameters which mark the positions of phase boundaries between states of different quantum order, as well as for the critical indices associated with the singular behaviour near these transition points of various physical quantities.
The coupled cluster method (CCM) has become one of the most pervasive of all ab initio formulations of quantum many-body theory.It has yielded numerical results which are among the most accurate available for a wide range of both nite and extended physical systems de ned on a spatial continuum.This widespread success has spurred many recent applications to quantum systems de ned on a lattice.We discuss here a typical example of a two-dimensional spin-half Heisenberg magnet with two kinds of nearest-neighbour bonds.We show how the CCM can successfully describe the in uence of strong quantum uctuations on the zero-temperature phases and their quantum phase transitions.The model shows how the CCM can successfully describe the eects of competition between magnetic bonds with and without the presence of frustration.The frustrated case is particulary important since many other methods, including quantum Monte Carlo simulations, typical fail in this regime.