The anisotropic Heisenberg model close to the Ising limit: triangular lattice vs. effective models

Abstract

Stimulated by recent experiments on materials representing the realization of the anisotropic Heisenberg spin-$1/2$ model on the triangular lattice, we explore further properties of such a model in the easy-axis regime $\alpha =J_{\perp }/J_z<1$ and the plausibility of finding effective models that capture similar physics. We show that, at finite fields, the magnetization curve as well as the transverse magnetization (superfluid) order parameter $m_{\perp }$ of the triangular lattice model are indeed qualitatively reproduced by anisotropic Heisenberg models on the honeycomb or the square lattice. At the point of correspondence to the zero-field triangular lattice model, however, the bipartite models are qualitatively different as they remain gapless even at $\alpha \ll 1$ with a small but finite $m_{\perp }>0$. Conversely, we present several additional numerical studies of the full model on the triangular lattice which support the appearance of a gap at zero field and $\alpha \ll 1$. In particular, the magnetization curve $m(h)$ as well as the spin stiffness ${\rho }_s$ indicate a transition/crossover from gappless to gapped regimes at $\alpha \sim {\alpha }^{\ast }$ with ${\alpha }^{\ast }\lesssim 0.5$. We also show that deviations from the linear spin-wave theory and the emergence of the gap can be traced back to the strong effective repulsion between magnon excitations, showcasing similarity to strongly correlated systems.

References in corpus (32)

• Linear spin wave theory for single-Q incommensurate magnetic structures
• Long range Neel order in the triangular Heisenberg model
• Supersolids: what and where are they ?
• Exact spectra, spin susceptibilities and order parameter of the quantum Heisenberg antiferromagnet on the triangular lattice
• Supersolid hardcore bosons on the triangular lattice
• Neel order in square and triangular lattice Heisenberg models
• Supersolid Order from Disorder: Hard-Core Bosons on the Triangular Lattice
• Spin-waves in triangular lattice antiferromagnet: decays, spectrum renormalization, and singularities
• Persistent supersolid phase of hard-core bosons on the triangular lattice
• Quantum Phase Diagram of the Triangular-Lattice XXZ Model in a Magnetic Field
• Supersolid phase of hardcore bosons on triangular lattice
• Giant Magnetocaloric Effect in Spin Supersolid Candidate Na${}_2$BaCo(PO${}_4$)${}_2$
• Magnetization plateaus in frustrated antiferromagnetic quantum spin models
• Possible itinerant excitations and quantum spin state transitions in the effective spin-1/2 triangular-lattice antiferromagnet Na${}_2$BaCo(PO${}_4$)${}_2$
• Quantum spin liquid in the Ising triangular-lattice antiferromagnet neodymium heptatantalate
• The phase diagram of the antiferromagnetic XXZ model on the triangular lattice
• A Comparative Study of the Magnetization Process of Two-Dimensional Antiferromagnets
• Extended supersolid phase of frustrated hard-core bosons on a triangular lattice
• Spin Supersolidity in Nearly Ideal Easy-axis Triangular Quantum Antiferromagnet Na${}_2$BaCo(PO${}_4$)${}_2$
• Supersolid Order of Frustrated Hard-Core Bosons in a Triangular Lattice System
• Direct calculation of the spin stiffness on square, triangular and cubic lattices using the coupled cluster method
• Continuum excitations in a spin-supersolid on a triangular lattice
• Direct Calculation of Spin-Stiffness for Spin-1/2 Heisenberg Models
• Classical and quantum two-dimensional anisotropic Heisenberg antiferromagnets
• Finite-temperature properties of the easy-axis Heisenberg model on frustrated lattices
• Double Magnon-Roton Excitations in the Triangular-Lattice Spin Supersolid
• Phase Diagram of the Easy-Axis Triangular-Lattice $J_1-J_2$ Model
• Simulating Spin Dynamics of Supersolid States in a Quantum Ising Magnet
• Wannier states and spin supersolid physics in the triangular antiferromagnet K${}_2$Co(SeO${}_3$)${}_2$
• Easy-axis Heisenberg model on the triangular lattice: from supersolid to gapped solid
• XDiag: Exact Diagonalization for Quantum Many-Body Systems
• Non-linear spin wave theory in the strong easy-axis limit of the triangular XXZ model

Cited by in corpus (1)

• Dissipationless dynamics of spin supersolid states in a spin-1/2 triangular antiferromagnet with impurities