Spin dynamics of counterrotating Kitaev spirals via duality

Incommensurate spiral order is a common occurrence in frustrated magnetic insulators. Typically, all magnetic moments rotate uniformly, through the same wavevector. However the honeycomb iridates family Li2IrO3 shows an incommensurate order where spirals on neighboring sublattices are counter-rotating, giving each moment a different local environment. Theoretically describing its spin dynamics has remained a challenge: the Kitaev interactions proposed to stabilize this state, which arise from strong spin-orbit effects, induce magnon umklapp scattering processes in spin-wave theory. Here we propose an approach via a (Klein) duality transformation into a conventional spiral of a frustrated Heisenberg model, allowing a direct derivation of the dynamical structure factor. We analyze both Kitaev and Dzyaloshinskii-Moriya based models, both of which can stabilize counterrotating spirals, but with different spin dynamics, and we propose experimental tests to identify the origin of counterrotation.Comment: 4 pages, 3 figures; appendix 5 pages, 2 figure

Valence Bonds in Random Quantum Magnets: Theory and Application to YbMgGaO4

We analyze the effect of quenched disorder on spin-1/2 quantum magnets in which magnetic frustration promotes the formation of local singlets. Our results include a theory for 2d valence-bond solids subject to weak bond randomness, as well as extensions to stronger disorder regimes where we make connections with quantum spin liquids. We find, on various lattices, that the destruction of a valence-bond solid phase by weak quenched disorder leads inevitably to the nucleation of topological defects carrying spin-1/2 moments. This renormalizes the lattice into a strongly random spin network with interesting low-energy excitations. Similarly when short-ranged valence bonds would be pinned by stronger disorder, we find that this putative glass is unstable to defects that carry spin-1/2 magnetic moments, and whose residual interactions decide the ultimate low energy fate. Motivated by these results we conjecture Lieb-Schultz-Mattis-like restrictions on ground states for disordered magnets with spin-1/2 per statistical unit cell. These conjectures are supported by an argument for 1d spin chains. We apply insights from this study to the phenomenology of YbMgGaO$_4$, a recently discovered triangular lattice spin-1/2 insulator which was proposed to be a quantum spin liquid. We instead explore a description based on the present theory. Experimental signatures, including unusual specific heat, thermal conductivity, and dynamical structure factor, and their behavior in a magnetic field, are predicted from the theory, and compare favorably with existing measurements on YbMgGaO$_4$ and related materials.Comment: v2: Stylistic revisions to improve clarity. 22 pages, 8 figures, 2 tables main text; 13 pages, 3 figures appendice

Minimal models for topological Weyl semimetals

Topological Weyl semimetals (TWS) can be classified as type-I TWS, in which the density of states vanishes at the Weyl nodes, and type-II TWS where an electron and a hole pocket meet with finite density of states at the nodal energy. The dispersions of type-II Weyl nodes are tilted and break Lorentz invariance, allowing for physical properties distinct from those in a type-I TWS. We present minimal lattice models for both time-reversal-breaking and inversion-breaking type-II Weyl semimetals, and investigate their bulk properties and topological surface states. These lattice models capture the extended Fermi pockets and the connectivities of Fermi arcs. In addition to the Fermi arcs, which are topologically protected, we identify surface "track states" that arise out of the topological Fermi arc states at the transition from type-I to type-II with multiple Weyl nodes, and persist in the type-II TWS.Comment: 13 pages, 9 figure

Topological Crystalline Bose Insulator in Two Dimensions via Entanglement Spectrum

Strongly correlated analogues of topological insulators have been explored in systems with purely on-site symmetries, such as time-reversal or charge conservation. Here, we use recently developed tensor network tools to study a quantum state of interacting bosons which is featureless in the bulk, but distinguished from an atomic insulator in that it exhibits entanglement which is protected by its spatial symmetries. These properties are encoded in a model many-body wavefunction that describes a fully symmetric insulator of bosons on the honeycomb lattice at half filling per site. While the resulting integer unit cell filling allows the state to bypass `no-go' theorems that trigger fractionalization at fractional filling, it nevertheless has nontrivial entanglement, protected by symmetry. We demonstrate this by computing the boundary entanglement spectra, finding a gapless entanglement edge described by a conformal field theory as well as degeneracies protected by the non-trivial action of combined charge-conservation and spatial symmetries on the edge. Here, the tight-binding representation of the space group symmetries plays a particular role in allowing certain entanglement cuts that are not allowed on other lattices of the same symmetry, suggesting that the lattice representation can serve as an additional symmetry ingredient in protecting an interacting topological phase. Our results extend to a related insulating state of electrons, with short-ranged entanglement and no band insulator analogue.Comment: 18 pages, 13 figures Added additional reference

Robust non-Abelian spin liquid and possible intermediate phase in antiferromagnetic Kitaev model with magnetic field

We investigate the non-Abelian topological chiral spin liquid phase in the two-dimensional (2D) Kitaev honeycomb model subject to a magnetic field. By combining density matrix renormalization group (DMRG) and exact diagonalization (ED) we study the energy spectra, entanglement, topological degeneracy, and expectation values of Wilson loop operators, allowing for robust characterization. While the ferromagnetic (FM) Kitaev spin liquid is already destroyed by a weak magnetic field with Zeeman energy $H_*^\text{FM} \approx 0.02$, the antiferromagnetic (AFM) spin liquid remains robust up to a magnetic field that is an order of magnitude larger, $H_*^\text{AFM} \approx 0.2$. Interestingly, for larger fields $H_*^\text{AFM} < H < H_{**}^\text{AFM}$, an intermediate gapless phase is observed, before a second transition to the high-field partially-polarized paramagnet. We attribute this rich phase diagram, and the remarkable stability of the chiral topological phase in the AFM Kitaev model, to the interplay of strong spin-orbit coupling and frustration enhanced by the magnetic field. Our findings suggest relevance to recent experiments on RuCl$_3$ under magnetic fields.Comment: 8 pages, 8 figure

Quark masses : an environmental impact statement

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Physics, 2008.Includes bibliographical references (leaves 63-65).We investigate how the requirement that organic chemistry be possible constrains the values of the quark masses. Specifically, we choose a slice through the parameter space of the Standard Model in which quark masses vary so that as many as three quarks play a role in the formation of nuclei, while keeping fixed the average mass of the two lightest baryons (in units of the electron mass) and the strength of the low-energy nuclear interaction. We classify universes on that slice as congenial if they contain stable nuclei with electric charge 1 and 6 (thus making organic chemistry possible in principle). Universes that lack one or both such stable nuclei are classified as uncongenial. We reassess the relationship between baryon masses and quark masses, using information in baryon mass differences in our world and the pion-nucleon sigma term [sigma]IIN. We generalize the Weizsacker semi-empirical mass formula through a degenerate Fermi gas model that handles the kinetic energy of new baryonic species as they begin to participate in the nucleus, and derive an expression for the asymmetry energy equivalent in the SU(3) limit through a minimization procedure on the quadratic Casimir operator. We spell out the conditions for decay by weak nucleon emission. Finally, we study the congeniality of various regions in the quark mass space, primarily by direct comparison to analog nuclei in our universe. Considering only two light quarks u and d, we find a band of congeniality roughly 29 MeV wide in mu - md, with our universe living comfortably away from the edge. We find multiple congeniality regions in the three quark mass space. For an important region around the SU(3) limit, we have not determined conclusive results but we have constructed the machinery to aid in its analysis and formulated the relevant problems. We have succeeded in formulating a well defined question about congeniality, and have made concrete progress toward answering it.by Itamar Kimchi.S.B