Dynamical structure factor of the triangular antiferromagnet: Schwinger boson theory beyond mean field

Abstract

We compute the zero temperature dynamical structure factor S(q, ω) of the triangular lattice Heisenberg model (TLHM) using a Schwinger boson approach that includes the Gaussian fluctuations (1/N corrections) of the saddle point solution. While the ground state of this model exhibits a well-known 120 • magnetic ordering, experimental observations have revealed a strong quantum character of the excitation spectrum. We conjecture that this phenomenon arises from the proximity of the ground state of the TLHM to the quantum melting point separating the magnetically ordered and spin liquid states. Within this scenario, magnons are described as collective modes (two spinonbound states) of a spinon condensate (Higgs phase) that spontaneously breaks the SU(2) symmetry of the TLHM. Crucial to our results is the proper account of this spontaneous symmetry breaking. The main qualitative difference relative to semi-classical treatments (1/S expansion) is the presence of a high-energy spinon continuum extending up to about three times the single-magnon bandwidth. In addition, the magnitude of the ordered moment (m = 0.224) agrees very well with numerical results and the low energy part of the single-magnon dispersion is in very good agreement with series expansions. Our results indicate that the Schwinger boson approach is an adequate starting point for describing the excitation spectrum of some magnetically ordered compounds that are near the quantum melting point separating this Higgs phase from the deconfined spin liquid state. arXiv:1802.06878v4 [cond-mat.str-el]

Large- S limit of the large- N theory for the triangular antiferromagnet

“…In Ref. 37 we demonstrated that, even for S = 1/2 (quantum limit), the spin velocities of these poles basically coincide with the spin-wave velocities obtained from LSWT plus 1/S corrections. 35,38,39 In this work we demonstrate these poles coincide over the full Brillouin zone with the ones obtained from LSWT in the S → ∞ limit.…”

“…The After introducing the Hubbard-Stratonovich (HS) transformations that decouple the AA and BB terms, 37 the partition function becomes…”

“…G sp is the saddle point Green function and v α = ∂G −1 ∂φα is the so-called internal vertex. S (0) coincides with the effective action S sp eff evaluated at the SP solution, so the effective action can be rewritten as 12,37…”

Spin liquids in geometrically perfect triangular antiferromagnets

“…Already the first theoretical studies of spin dynamics exposed salient deviations from non-interacting magnon scenario of linear spin-wave theory. Not only the spin waves are renormalized, sometimes changing their shape to produce roton minima around the M -points [84][85][86], but also the spectrum is washed out into a broad continuum at energies ω > J 1 [86][87][88][89]. These findings were initially interpreted as signatures of spinon excitationsan idea inspired by the work on square-lattice Heisenberg antiferromagnets.…”

Spin functional renormalization group for quantum Heisenberg ferromagnets: Magnetization and magnon damping in two dimensions

“…However, going beyond the mean-field approximation is rather difficult within the Schwinger boson approach. [27][28][29][30] Another analytical approach to quantum ferromagnets is based on the decoupling of the equations of motion for the Green functions of the spins. [31][32][33] Of course, the physical properties of quantum ferromagnets can be obtained with high accuracy numerically using Monte Carlo simulations.…”