John Chalker

Abstract:

We analyze the dynamical response of a range of three-dimensional Kitaev quantum spin liquids, using lattice models chosen to explore the different possible low-energy spectra for gapless Majorana fermions, with either Fermi surfaces, nodal lines, or Weyl points. We find that the behavior of the dynamical structure factor is distinct in all three cases, reflecting the quasiparticle density of states in two fundamentally different ways. First, the low-energy response is either straightforwardly related to the power with which the low-energy density of states vanishes; or for a nonvanishing density of states, to the phase shifts encountered in the corresponding x-ray edge problem, whose phenomenology we extend to the case of Majorana fermions. Second, at higher energies, there is a rich fine structure, determined by microscopic features of the Majorana spectrum. Our theoretical results test the usefulness of inelastic neutron scattering as a probe of these quantum spin liquids: we find that although spin flips fractionalize, the main features of the dynamical spin response nevertheless admit straightforward interpretations in terms of Majorana and flux loop excitations.

Abstract:

We study Ising antiferromagnets that have nearest-neighbour interactions on multilayer triangular lattices with frustrated (abc and abab) stacking, and make comparisons with the unfrustrated (aaa) stacking. If interlayer couplings are much weaker than in-plane ones, the paramagnetic phase of models with frustrated stackings has a classical spin-liquid regime at low temperature, in which correlations are strong both within and between planes, but there is no long-range order. We investigate this regime using Monte Carlo simulations and by mapping the spin models to coupled height models, which are treated using renormalisation group methods and an analysis of the effects of vortex excitations. The classical spin-liquid regime is parametrically wide at small interlayer coupling in models with frustrated stackings. By contrast, for the unfrustrated stacking there is no extended regime in which interlayer correlations are strong without three-dimensional order.

Abstract:

We examine the dynamics of a single hole in the gapless phase of the Kitaev honeycomb model, focusing on the slow-hole regime where the bare hopping amplitude t is much less than the Kitaev exchange energy J. In this regime, the hole does not generate gapped flux excitations and is dressed only by the gapless fermion excitations. Investigating the single-hole spectral function, we find that the hole propagates coherently with a quasiparticle weight that is finite but approaches zero as t/J → 0. This conclusion follows from two approximate treatments, which capture the same physics in complementary ways. Both treatments use the stationary limit as an exactly solvable starting point to study the spectral function approximately (i) by employing a variational approach in terms of a trial state that interpolates between the limits of a stationary hole and an infinitely fast hole and (ii) by considering a special point in the gapless phase that corresponds to a simplified one-dimensional problem.

Abstract:

We show numerically that the “deconfined” quantum critical point between the Neel antiferromagnet ´ and the columnar valence-bond solid, for a square lattice of spin 1=2, has an emergent SO(5) symmetry. This symmetry allows the Neel vector and the valence-bond solid order parameter to be rotated into each ´ other. It is a remarkable (2 þ 1)-dimensional analogue of the SOð4Þ¼½SUð2Þ × SUð2Þ=Z2 symmetry that appears in the scaling limit for the spin-1=2 Heisenberg chain. The emergent SO(5) symmetry is strong evidence that the phase transition in the (2 þ 1)-dimensional system is truly continuous, despite the violations of finite-size scaling observed previously in this problem. It also implies surprising relations between correlation functions at the transition. The symmetry enhancement is expected to apply generally to the critical two-component Abelian Higgs model (noncompact CP1 model). The result indicates that in three dimensions there is an SO(5)-symmetric conformal field theory that has no relevant singlet operators, so is radically different from conventional Wilson-Fisher-type conformal field theories.