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arXiv:2008.08751 · Physical review. B./Physical review. B

Exact diagonalization study of the anisotropic Heisenberg model related to YbMgGaO4

Muwei Wu, Dao‐Xin Yao, Han-Qing Wu

Published May 13, 2021• 16 citations
arXivHTMLPDF

Abstract

Employing exact diagonalization, we systematically study the anisotropic Heisenberg model which is related to rare-earth triangular-lattice materials. We probe its full 3D phase diagram afresh and identify a large region of quantum spin liquid (QSL) phase which can extend to the QSL region of the ${J}_{1}\text{--}{J}_{2}$ triangular Heisenberg model. Furthermore, we explore the magnetization curves of different phases and reproduce the 1/3-magnetization plateau in the quantum spin liquid phase region. More importantly, to study the possible chemical disorders in real materials, we consider the randomness of exchange interactions and find no spin glass order. And there is a large region of random-singlet phase which contains strongly random spin networks, dominated by two-spin singlets, four-spin singlets and other singlet domains. Our comprehensive ED study can give detailed insightful understanding of the microscopic Hamiltonian related to the ${\mathrm{YbMgGaO}}_{4}$ and some other related rare-earth triangular-lattice materials.

DOI
10.1103/physrevb.103.205122

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Employing exact diagonalization, we systematically study the anisotropic Heisenberg model which is related to rare-earth triangular-lattice materials. We probe its full 3D phase diagram afresh and identify a large region of quantum spin liquid (QSL) phase which can extend to the QSL region of the J1–J2{J}_{1}\text{--}{J}_{2}J1​–J2​ triangular Heisenberg model. Furthermore, we explore the magnetization curves of different phases and reproduce the 1/3-magnetization plateau in the quantum spin liquid phase region. More importantly, to study the possible chemical disorders in real materials, we consider the randomness of exchange interactions and find no spin glass order. And there is a large region of random-singlet phase which contains strongly random spin networks, dominated by two-spin singlets, four-spin singlets and other singlet domains. Our comprehensive ED study can give detailed insightful understanding of the microscopic Hamiltonian related to the YbMgGaO4{\mathrm{YbMgGaO}}_{4}YbMgGaO4​ and some other related rare-earth triangular-lattice materials.
Using Lanczos exact diagonalization (ED), we study the spin-1/2 ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model with the four-spin ring-exchange interaction Jr{J}_{r}Jr​ on a triangular lattice. We mainly use the level spectroscopic technique of two 36-site tori to investigate the ground-state phase diagram, and further characterize phases by spin, dimer, and chiral correlation functions. The ground state has rich phases including several magnetic-ordered phases like the zigzag phase and tetrahedral phase, as well as several novel nonmagnetic phases, some of which exhibit valence bond solid behavior in their dimer correlation functions. However, we do not find direct evidence of a quantum spin liquid phase with spinon Fermi surface in this model. Our results can give a better understanding of the ground-state properties of the triangular Heisenberg model with ring-exchange interaction and help to understand the relevant triangular materials.
We study the effects of bond randomness in the spin-1/21/21/2 ${J}_{1}\ensuremath{-}{J}_{2}$ triangular Heisenberg model using exact diagonalization and density-matrix renormalization group. With increasing bond randomness, we identify a randomness-induced spin-liquid-like phase without any magnetic order, dimer order, spin-glass order, or valence-bond-glass order. The finite-size scaling of gaps suggests the gapless nature of both spin triplet and singlet excitations, which is further supported by the broad continuum of the dynamical spin structure factor. By studying the bipartite entanglement spectrum of the system on cylinder geometry, we identify the features of the low-lying entanglement spectrum in the spin-liquid-like phase, which may distinguish this randomness-induced spin-liquid-like phase and the intrinsic spin-liquid phase in the clean ${J}_{1}\ensuremath{-}{J}_{2}$ triangular Heisenberg model. We further discuss the nature of this spin-liquid-like phase and the indication of our results for understanding spin-liquid-like materials with triangular-lattice structure.
Dynamics and stability of U(1) spin liquids beyond mean-field theory: Triangular-lattice J1J_1J1​-J2J_2J2​ Heisenberg model
Quantum spin liquids (QSLs) are long-range entangled phases of frustrated magnets exhibiting fractionalised spin excitations. In two dimensions, there is limited analytical understanding of their excitation spectra beyond parton mean-field theories, which fail to capture many features of the finite frequency dynamical response. We use a self-consistent mean-field theory combined with the random phase approximation (RPA) for the J1J_1J1​-J2J_2J2​ Heisenberg model on the triangular lattice to describe the strong spinon-spinon interactions of the U(1) Dirac QSL. We obtain quantitative results for the dynamical spin structure factor and phase diagram compatible with comprehensive numerical efforts. We show the continuum response at the Brillouin zone corners is described by a spinon-exciton hybridised with monopole gauge excitations. We further show that the transition from the QSL to 120-degree coplanar order is in the QED3_33​ O(3)-GN universality class. We extend the method to chiral QSLs and XXZ anisotropy, and discuss its broad range of applicability to other models and for describing inelastic neutron scattering experiments in KYbSe2_22​.
Based on exact diagonalization and density matrix renormalization group method, we show that an anisotropic triangular lattice Heisenberg spin model has three distinct quantum phases. In particular, a spin-liquid phase is present in the weak interchain coupling regime, which is characterized by an anisotropic spin structure factor with an exponential-decay spin correlator along the weaker coupling direction, consistent with the Cs2CuCl4{\mathrm{Cs}}_{2}\mathrm{Cu}{\mathrm{Cl}}_{4}Cs2​CuCl4​ compounds. In the obtained phase diagram, the spin-liquid phase is found to persist up to a relatively large critical anisotropic coupling ratio ${J}^{\ensuremath{'}}∕J=0.78$, which is stabilized by strong quantum fluctuations, with a parity symmetry distinct from two magnetic ordered states in the stronger coupling regime.
Spin liquids are important for a fundamental understanding of quantum magnetism and may find applications in quantum computing, but it is still not clear under which general circumstances these exotic, quantum-disordered phases occur. To gather deeper insights, we analyze a generalization of the spatially anisotropic triangular lattice (SATL), the spatially completely anisotropic triangular lattice (SCATL), using Takahashi's modified spin-wave theory, complemented by exact diagonalizations. For Heisenberg interactions, calculations on the SATL predict quantum disorder for several materials in which experiments have found magnetic long-range order. In the SCATL, the corresponding parameter values yield ordered ground states and this discrepancy disappears. We also study the model with XYXYXY interactions, which can be implemented with current technology in ultracold atoms in optical lattices. This allows to estimate the stability of quantum-disordered phases towards imperfect implementations of the coupling parameters. For both kinds of interactions, we find indications for extended quantum-disordered phases. In part of the parameter space of the XYXYXY model, exact diagonalization hints at a gapped state with chiral long-range order. In both models, our results suggest that two gapped nonmagnetic regions, identified as distinct in the SATL, could actually be continuously connected via the additional anisotropy of the SCATL. Further, we find that different kinds of order are always separated by disordered phases. We propose that this is a quite universal feature of two-dimensional frustrated antiferromagnets with continuous symmetry in the couplings. The SCATL may therefore---besides being relevant for experiments---yield fundamental insight into quantum-disordered phases.
Motivated by a recent experiment on the rare-earth material YbMgGaO4{\mathrm{YbMgGaO}}_{4}YbMgGaO4​ [Y. Li et al., Phys. Rev. Lett. 115, 167203 (2015)], which found that the ground state of YbMgGaO4{\mathrm{YbMgGaO}}_{4}YbMgGaO4​ is a quantum spin liquid, we study the ground-state phase diagram of an anisotropic spin-1/21/21/2 model that was proposed to describe YbMgGaO4{\mathrm{YbMgGaO}}_{4}YbMgGaO4​. Using the density matrix renormalization-group method in combination with the exact-diagonalization method, we calculate a variety of physical quantities, including the ground-state energy, the fidelity, the entanglement entropy and spin-spin correlation functions. Our studies show that in the quantum phase diagram, there is a ${120}^{\ensuremath{\circ}}$ phase and two distinct stripe phases. The transitions from the two stripe phases to the ${120}^{\ensuremath{\circ}}$ phase are of the first order. However, the transition between the two stripe phases is not of the first order, which is different from its classical counterpart. Additionally, we find no evidence for a quantum spin liquid in this model. Our results suggest that additional terms may also be important to model the material YbMgGaO4{\mathrm{YbMgGaO}}_{4}YbMgGaO4​. These findings will stimulate further experimental and theoretical works in understanding the quantum spin-liquid ground state in YbMgGaO4{\mathrm{YbMgGaO}}_{4}YbMgGaO4​.