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

TL;DR

This paper uses an advanced Schwinger boson approach to compute the dynamical structure factor of the triangular lattice Heisenberg model, revealing a high-energy spinon continuum and aligning well with experimental and numerical data.

Contribution

It extends the Schwinger boson theory beyond mean field by including Gaussian fluctuations, capturing quantum effects near the spin liquid transition.

Findings

Presence of a high-energy spinon continuum up to three times the magnon bandwidth

Ordered moment magnitude matches numerical results (m=0.224)

Low energy dispersion agrees with series expansion results

Abstract

We compute the zero temperature dynamical structure factor $S({\bf q},\omega)$ 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$^{\circ}$ 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 spinon-bound 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 {\it deconfined} spin liquid state.