Dynamical Axions in U(1) Quantum Spin Liquids.

Since their proposal nearly half a century ago, physicists have sought axions in both high energy and condensed matter settings. Despite intense and growing efforts, to date, experimental success has been limited, with the most prominent results arising in the context of topological insulators. Here, we propose a novel mechanism whereby axions can be realized in quantum spin liquids. We discuss the necessary symmetry requirements and identify possible experimental realizations in candidate pyrochlore materials. In this context, the axions couple to both the external and the emergent electromagnetic fields. We show that the interaction between the axion and the emergent photon leads to a characteristic dynamical response, which can be measured experimentally in inelastic neutron scattering. This Letter sets the stage for studying axion electrodynamics in the highly tunable setting of frustrated magnets.

Emergent Fine Structure Constant of Quantum Spin Ice Is Large.

Condensed-matter systems provide alternative "vacua" exhibiting emergent low-energy properties drastically different from those of the standard model. A case in point is the emergent quantum electrodynamics (QED) in the fractionalized topological magnet known as quantum spin ice, whose magnetic monopoles set it apart from the familiar QED of the world we live in. Here, we show that the two greatly differ in their fine structure constant α, which parametrizes how strongly matter couples to light: α_{QSI} is more than an order of magnitude greater than α_{QED}≈1/137. Furthermore, α_{QSI}, the emergent speed of light, and all other parameters of the emergent QED, are tunable by engineering the microscopic Hamiltonian. We find that α_{QSI} can be tuned all the way from zero up to what is believed to be the strongest possible coupling beyond which QED confines. In view of the small size of its constrained Hilbert space, this marks out quantum spin ice as an ideal platform for studying exotic quantum field theories and a target for quantum simulation. The large α_{QSI} implies that experiments probing candidate condensed-matter realizations of quantum spin ice should expect to observe phenomena arising due to strong interactions.

The ß Fermi-Pasta-Ulam-Tsingou recurrence problem.

We perform a thorough investigation of the first Fermi-Pasta-Ulam-Tsingou (FPUT) recurrence in the ß-FPUT chain for both positive and negative ß. We show numerically that the rescaled FPUT recurrence time Tr=tr/(N+1)3 depends, for large N, only on the parameter S≡Eß(N+1). Our numerics also reveal that for small |S|, Tr is linear in S with positive slope for both positive and negative ß. For large |S|, Tr is proportional to |S|-1/2 for both positive and negative ß but with different multiplicative constants. We numerically study the continuum limit and find that the recurrence time closely follows the |S|-1/2 scaling and can be interpreted in terms of solitons, as in the case of the KdV equation for the α chain. The difference in the multiplicative factors between positive and negative ß arises from soliton-kink interactions that exist only in the negative ß case. We complement our numerical results with analytical considerations in the nearly linear regime (small |S|) and in the highly nonlinear regime (large |S|). For the former, we extend previous results using a shifted-frequency perturbation theory and find a closed form for Tr that depends only on S. In the latter regime, we show that Tr∝|S|-1/2 is predicted by the soliton theory in the continuum limit. We then investigate the existence of the FPUT recurrences and show that their disappearance surprisingly depends only on Eß for large N, not S. Finally, we end by discussing the striking differences in the amount of energy mixing between positive and negative ß and offer some remarks on the thermodynamic limit.

Behavior and breakdown of higher-order Fermi-Pasta-Ulam-Tsingou recurrences.

We numerically investigate the existence and stability of higher-order recurrences (HoRs), including super-recurrences, super-super-recurrences, etc., in the α and ß Fermi-Pasta-Ulam-Tsingou (FPUT) lattices for initial conditions in the fundamental normal mode. Our results represent a considerable extension of the pioneering work of Tuck and Menzel on super-recurrences. For fixed lattice sizes, we observe and study apparent singularities in the periods of these HoRs, speculated to be caused by nonlinear resonances. Interestingly, these singularities depend very sensitively on the initial energy and the respective nonlinear parameters. Furthermore, we compare the mechanisms by which the super-recurrences in the two models breakdown as the initial energy and respective nonlinear parameters are increased. The breakdown of super-recurrences in the ß-FPUT lattice is associated with the destruction of the so-called metastable state and thus with relaxation towards equilibrium. For the α-FPUT lattice, we find this is not the case and show that the super-recurrences break down while the lattice is still metastable and far from equilibrium. We close with comments on the generality of our results for different lattice sizes.