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Abstract:

We propose a simple family of valence-bond crystals as potential ground states of the S=1/2 and S=1 Heisenberg antiferromagnet on the pyrochlore lattice. Exponentially numerous in the linear size of the system, these can be visualized as hard-hexagon coverings, with each hexagon representing a resonating valence-bond ring. This ensemble spontaneously breaks rotation, inversion, and translation symmetries. A simple, yet accurate, variational wave function allows a precise determination of the energy, confirmed by the density matrix renormalization group and numerical linked cluster expansion, and extended by an analysis of excited states. The identification of the origin of the stability indicates applicability to a broad class of frustrated lattices, which we demonstrate for the checkerboard and ruby lattices. Our work suggests a perspective on such quantum magnets, in which unfrustrated motifs are effectively uncoupled by the frustration of their interactions.

Abstract:

Point-like topological defects are singular configurations that manifest in and out of various equilibrium systems with two-dimensional orientational order. Because they are associated with a nonzero circuitation condition, the presence of defects induces a long-range perturbation of the orientation landscape around them. The effective dynamics of defects is thus generally described in terms of quasi-particles interacting via the orientation field they produce, whose evolution in the simplest setting is governed by the diffusion equation. Because of the multivalued nature of the orientation field, its expression for a defect moving with an arbitrary trajectory cannot be determined straightforwardly and is often evaluated in the quasi-static approximation. Here, we instead derive the exact expression for the orientation created by multiple moving defects, which we find to depend on their past trajectories and thus to be nonlocal in time. Performing various expansions in relevant regimes, we demonstrate how improved approximations with respect to the quasi-static defect solution can be obtained. Moreover, our results lead to so far unnoticed structures in the orientation field of moving defects, which we discuss in light of existing experimental results

Abstract:

We theoretically and computationally study the low-Reynolds-number hydrodynamics of a linear active microswimmer surfing on a compressible thin fluid layer characterized by an odd viscosity. Since the underlying three-dimensional fluid is assumed to be very thin compared to any lateral size of the fluid layer, the model is effectively two-dimensional. In the limit of small odd viscosity compared to the even viscosities of the fluid layer, we obtain analytical expressions for the self-induced flow field, which includes non-reciprocal components due to the odd viscosity. On this basis, we fully analyze the behavior of a single linear swimmer, finding that it follows a circular path, the radius of which is, to leading order, inversely proportional to the magnitude of the odd viscosity. In addition, we show that a pair of swimmers exhibits a wealth of two-body dynamics that depends on the initial relative orientation angles as well as on the propulsion mechanism adopted by each swimmer. In particular, the pusher-pusher and pusher-puller-type swimmer pairs exhibit a generic spiral motion, while the puller-puller pair is found to either co-rotate in the steady state along a circular trajectory or exhibit a more complex chaotic behavior resulting from the interplay between hydrodynamic and steric interactions. Our theoretical predictions may pave the way toward a better understanding of active transport in active chiral fluids with odd viscosity, and may find potential applications in the quantitative microrheological characterization of odd-viscous fluids.Comment: 21 pages, 8 figure