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]

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By considering an extended double-exchange model with spin-orbit coupling (SOC), we derive a general form of the Berry phase γ that electrons pick up when moving around a closed loop. This form generalizes the well-known result valid for SU(2) invariant systems, γ = Ω/2, where Ω is the solid angle subtended by the local magnetic moments enclosed by the loop. The general form of γ demonstrates that collinear and coplanar magnetic textures can also induce a Berry phase different from 0 or π, smoothly connecting the result for SU(2) invariant systems with the well-known result of Karplus and Luttinger for collinear ferromagnets with finite SOC. By taking the continuum limit of the theory, we also derive the corresponding generalized form of the real space Berry curvature. The new expression is a generalization of the scalar spin chirality, which is presented in an explicitly covariant form. We finally show how these simple concepts can be used to understand the origin of the spontaneous topological Hall effect that has been recently reported in collinear and coplanar antiferromagnetic phases of correlated materials. arXiv:1909.13338v1 [cond-mat.str-el]

We introduce an extension of the Kitaev honeycomb model by including four-spin interactions that preserve the local gauge structure and hence the integrability of the original model. The extended model has a rich phase diagram containing five distinct vison crystals, as well as a symmetric π-flux spin liquid with a Fermi surface of Majorana fermions and a sequence of Lifshitz transitions. We discuss possible experimental signatures and, in particular, present finite-temperature Monte Carlo calculations of the specific heat and the static vison structure factor. We argue that our extended model emerges naturally from generic perturbations to the Kitaev honeycomb model.

Large-S and large-N theories (spin value S and spinor component number N ) are complementary, and sometimes conflicting, approaches to quantum magnetism. While large-S spin-wave theory captures the correct semiclassical behavior, large-N theories, on the other hand, emphasize the quantumness of spin fluctuations. In order to evaluate the possibility of the non-trivial recovery of the semiclassical magnetic excitations within a large-N approach, we compute the large-S limit of the dynamic spin structure of the triangular lattice Heisenberg antiferromagnet within a Schwinger boson spin representation. We demonstrate that, only after the incorporation of Gaussian (1/N ) corrections to the saddle-point (N = ∞) approximation, we are able to exactly reproduce the linear spin wave theory results in the large-S limit. The key observation is that the effect of 1/N corrections is to cancel out exactly the main contribution of the saddle-point solution; while the collective modes (magnons) consist of two spinon bound states arising from the poles of the RPA propagator. This result implies that it is essential to consider the interaction of the spinons with the emergent gauge fields and that the magnon dispersion relation should not be identified with that of the saddle-point spinons. arXiv:1905.10689v1 [cond-mat.str-el]