Schwinger boson theory of ordered magnets

Abstract

The Schwinger boson theory provides a natural path for treating quantum spin systems with large quantum fluctuations. In contrast to semi-classical treatments, this theory allows us to describe a continuous transition between magnetically ordered and spin liquid states, as well as the continuous evolution of the corresponding excitation spectrum. The square lattice Heisenberg antiferromagnet is one of the first models that was approached with the Schwinger boson theory. Here we revisit this problem to reveal several subtle points that were omitted in previous treatments and that are crucial to further develop this formalism. These points include the freedom for the choice of the saddle point (Hubbard-Stratonovich decoupling and choice of the condensate) and the $1/N$ expansion in the presence of a condensate. A key observation is that the spinon condensate leads to Feynman diagrams that include contributions of different order in $1/N$, which must be accounted to get a qualitatively correct excitation spectrum. We demonstrate that a proper treatment of these contributions leads to an exact cancellation of the single-spinon poles of the dynamical spin structure factor, as expected for a magnetically ordered state. The only surviving poles are the ones arising from the magnons (two-spinon bound states), which are the true collective modes of an ordered magnet.

arXiv comment25 pages, 12 figures

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• Complete field-induced spectral response of the spin-1/2 triangular-lattice antiferromagnet CsYbSe${}_2$
• Evidence of Two-Spinon Bound States in the Magnetic Spectrum of Ba${}_3$CoSb${}_2$O${}_9$
• Continuum of spin excitations in an ordered magnet
• Switching the Magnetization in Quantum Antiferromagnets
• Bilinear Majorana representations for spin operators with spin magnitudes $S>1/2$
• Modified large-$N$ approach to gapless spin liquids, magnetic orders, and dynamics: Application to triangular lattice antiferromagnets
• Exchange enhanced switching by alternating fields in quantum antiferromagnets
• Field-driven transition from quantum spin liquid to magnetic order in triangular-lattice antiferromagnets
• Schwinger-Keldysh non-perturbative field theory of open quantum systems beyond the Markovian regime: Application to spin-boson and spin-chain-boson models
• Field-Induced Magnon Decay, Magnon Shadows, and Roton-like Excitations in the Honeycomb Antiferromagnet YbBr${}_3$
• Confined and deconfined spinon excitations in the rectangular-lattice quantum antiferromagnet
• Order-by-disorder from Schwinger bosons in a frustrated honeycomb ferromagnet
• Thermal and quantum fluctuations in extended Kitaev-Yao-Lee spin-orbital model
• Multimagnon and multispinon $L_3$-edge RIXS spectra of an effective ${\tilde{J}}_1-{\tilde{J}}_2-{\tilde{J}}_3$ square lattice Heisenberg model