Spectrum of Itinerant Fractional Excitations in Quantum Spin Ice

We study the quantum dynamics of fractional excitations in quantum spin ice. We focus on the density of states in the two-monopole sector, rho(omega), as this can be connected to the wave-vector-integrated dynamical structure factor accessible in neutron scattering experiments. We find that rho(omega) exhibits a strikingly characteristic singular and asymmetric structure that provides a useful fingerprint for comparison to experiment. rho(omega) obtained from the exact diagonalization of a finite cluster agrees well with that, from the analytical solution of a hopping problem on a Husimi cactus representing configuration space, but not with the corresponding result on a face-centered cubic lattice, on which the monopoles move in real space. The main difference between the latter two lies in the inclusion of the emergent gauge field degrees of freedom, under which the monopoles are charged. This underlines the importance of treating both sets of degrees of freedom together, and it presents a novel instance of dimensional transmutation

The S=1/2S=1/2 Kagome Heisenberg Antiferromagnet Revisited

We examine the perennial quantum spin-liquid candidate $S=1/2$ Heisenberg antiferromagnet on the kagome lattice. Our study is based on achieving Lanczos diagonalization of the Hamiltonian on a $48$ site cluster in sectors with dimensions as a large as $5 \times 10^{11}$. The results reveal novel intricate structures in the low-lying energy spectrum. These structures by no means unambiguously support an emerging consensus of a $\mathbb{Z}_2$ spin liquid ground state, but instead appear compatible with several scenarios, including four-fold topological degeneracy, inversion symmetry breaking and a combination thereof. We discuss finite-size effects, such as the apparent absence of ETH, and note that while considerably reduced, some are still present for the largest cluster. Finally, we observe that an XXZ model in the Ising limit reproduces remarkably well the most striking features of finite-size spectra.Comment: 8 pages, 5 figure

Electron interactions in graphene in a strong magnetic field

Graphene in the quantum Hall regime exhibits a multi-component structure due to the electronic spin and chirality degrees of freedom. While the applied field breaks the spin symmetry explicitly, we show that the fate of the chirality SU(2) symmetry is more involved: the leading symmetry-breaking terms differ in origin when the Hamiltonian is projected onto the central (n=0) rather than any of the other Landau levels. Our description at the lattice level leads to a Harper equation; in its continuum limit, the ratio of lattice constant a and magnetic length l_B assumes the role of a small control parameter in different guises. The leading symmetry-breaking terms are direct (n=0) and exchange (n different from 0) terms, which are algebraically small in a/l_B. We comment on the Haldane pseudopotentials for graphene, and evaluate the easy-plane anisotropy of the graphene ferromagnet.Comment: 4 pages, 1 figure; revised version contains a more detailed comparison with experimental results; accepted for publication in PR

Symmetry Breaking on the Three-Dimensional Hyperkagome Lattice of Na_4Ir_3O_8

We study the antiferromagnetic spin-1/2 Heisenberg model on the highly frustrated, three-dimensional, hyperkagome lattice of Na_4Ir_3O_8 using a series expansion method. We propose a valence bond crystal with a 72 site unit cell as a ground state that supports many, very low lying, singlet excitations. Low energy spinons and triplons are confined to emergent lower-dimensional motifs. Here, and for analogous kagome and pyrochlore states, we suggest finite temperature signatures, including an Ising transition, in the magnetic specific heat due to a multistep breaking of discrete symmetries.Comment: 4 pages, 3 figure

Low-field behavior of an XY pyrochlore antiferromagnet: emergent clock anisotropies

Using $\rm Er_2Ti_2O_7$ as a motivation, we investigate finite-field properties of $XY$ pyrochlore antiferromagnets. In addition to a fluctuation-induced six-fold anisotropy present in zero field, an external magnetic field induces a combination of two-, three-, and six-fold clock terms as a function of its orientation providing for a rich and controllable magnetothermodynamics. For $\rm Er_2Ti_2O_7$, we predict a new phase transition for ${\bf H}\parallel [001]$. Re-entrant transitions are also found for ${\bf H}\parallel [111]$. We extend these results to the whole family the $XY$ pyrochlore antiferromagnets and show that presence and number of low-field transitions for different orientations can be used for locating a given material in the parameter space of anisotropic pyrochlores. Finite-temperature classical Monte Carlo simulations serve to confirm and illustrate these analytic predictions.Comment: 11 pages, accepted version with supplemental materia

Disorder by disorder and flat bands in the kagome transverse field Ising model

We study the transverse field Ising model on a kagome and a triangular lattice using high-order series expansions about the high-field limit. For the triangular lattice our results confirm a second-order quantum phase transition in the 3d XY universality class. Our findings for the kagome lattice indicate a notable instance of a disorder by disorder scenario in two dimensions. The latter follows from a combined analysis of the elementary gap in the high- and low-field limit which is shown to stay finite for all fields h. Furthermore, the lowest one-particle dispersion for the kagome lattice is extremely flat acquiring a dispersion only from order eight in the 1/h limit. This behaviour can be traced back to the existence of local modes and their breakdown which is understood intuitively via the linked cluster expansion.Comment: 11 pages, 11 figrue

Multifractality without fine-tuning in a Floquet quasiperiodic chain

Periodically driven, or Floquet, disordered quantum systems have generated many unexpected discoveries of late, such as the anomalous Floquet Anderson insulator and the discrete time crystal. Here, we report the emergence of an entire band of multifractal wavefunctions in a periodically driven chain of non-interacting particles subject to spatially quasiperiodic disorder. Remarkably, this multifractality is robust in that it does not require any fine-tuning of the model parameters, which sets it apart from the known multifractality of $critical$ wavefunctions. The multifractality arises as the periodic drive hybridises the localised and delocalised sectors of the undriven spectrum. We account for this phenomenon in a simple random matrix based theory. Finally, we discuss dynamical signatures of the multifractal states, which should betray their presence in cold atom experiments. Such a simple yet robust realisation of multifractality could advance this so far elusive phenomenon towards applications, such as the proposed disorder-induced enhancement of a superfluid transition.Comment: 22 pages, 13 figures, SciPost submissio

Nature of finite-temperature transition in anisotropic pyrochlore Er2Ti2O7

We study the finite-temperature transition in a model XY antiferromagnet on a pyrochlore lattice, which describes the pyrochlore material Er2Ti2O7. The ordered magnetic structure selected by thermal fluctuations is six-fold degenerate. Nevertheless, our classical Monte Carlo simulations show that the critical behavior corresponds to the three-dimensional XY universality class. We determine an additional critical exponent nu_6=0.75>nu characteristic of a dangerously irrelevant scaling variable. Persistent thermal fluctuations in the ordered phase are revealed in Monte Carlo simulations by the peculiar coexistence of Bragg peaks and diffuse magnetic scattering, the feature also observed in neutron diffraction experiments.Comment: 5+5 pages (including supplemental material