The boundary of a topological insulator (TI) hosts an anomaly restricting its possible phases: e.g. 3D strong and weak TIs maintain surface conductivity at any disorder if symmetry is preserved on-average, at least when electron interactions on the s
urface are weak. However the interplay of strong interactions and disorder with the boundary anomaly has not yet been theoretically addressed. Here we study this combination for the edge of a 2D TI and the surface of a 3D weak TI, showing how it can lead to an Anomalous Many Body Localized (AMBL) phase that preserves the anomaly. We discuss how the anomalous Kramers parity switching with pi flux arises in the bosonized theory of the localized helical state. The anomaly can be probed in localized boundaries by electrostatically sensing nonlinear hopping transport with e/2 shot noise. Our AMBL construction in 3D weak TIs fails for 3D strong TIs, suggesting that their anomaly restrictions are distinguished by strong interactions.
Recently measurements on various spin-1/2 quantum magnets such as H$_3$LiIr$_2$O$_6$, LiZn$_2$Mo$_3$O$_8$, ZnCu$_3$(OH)$_6$Cl$_2$ and 1T-TaS$_2$ -- all described by magnetic frustration and quenched disorder but with no other common relation -- never
theless showed apparently universal scaling features at low temperature. In particular the heat capacity C[H,T] in temperature T and magnetic field H exhibits T/H data collapse reminiscent of scaling near a critical point. Here we propose a theory for this scaling collapse based on an emergent random-singlet regime extended to include spin-orbit coupling and antisymmetric Dzyaloshinskii-Moriya (DM) interactions. We derive the scaling $C[H,T]/T sim H^{-gamma} F_q[T/H]$ with $F_q[x] = x^{q}$ at small $x$, with $q in$ (0,1,2) an integer exponent whose value depends on spatial symmetries. The agreement with experiments indicates that a fraction of spins form random valence bonds and that these are surrounded by a quantum paramagnetic phase. We also discuss distinct scaling for magnetization with a $q$-dependent subdominant term enforced by Maxwells relations.
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 extensi
ons 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.
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 spi
rals 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.
A family of insulating iridates with chemical formula Li$_2$IrO$_3$ has recently been discovered, featuring three distinct crystal structures $alpha,beta,gamma$ (honeycomb, hyperhoneycomb, stripyhoneycomb). Measurements on the three-dimensional polyt
ypes, $beta$- and $gamma$-Li$_2$IrO$_3$, found that they magnetically order into remarkably similar spiral phases, exhibiting a non-coplanar counter-rotating spiral magnetic order with equivalent q=0.57 wavevectors. We examine magnetic Hamiltonians for this family and show that the same triplet of nearest-neighbor Kitaev-Heisenberg-Ising (KJI) interactions reproduces this spiral order on both $beta,gamma$-Li$_2$IrO$_3$ structures. We analyze the origin of this phenomenon by studying the model on a 1D zigzag chain, a structural unit common to the three polytypes. The zigzag-chain solution transparently shows how the Kitaev interaction stabilizes the counter-rotating spiral, which is shown to persist on restoring the inter-chain coupling. Our minimal model makes a concrete prediction for the magnetic order in $alpha$-Li$_2$IrO$_3$.
Motivated by the recent synthesis of two insulating Li$_2$IrO$_3$ polymorphs, where Ir$^{4+}$ $S_{eff}$=1/2 moments form 3D (harmonic) honeycomb structures with threefold coordination, we study magnetic Hamiltonians on the resulting $beta$-Li$_2$IrO$
_3$ hyperhoneycomb lattice and $gamma$-Li$_2$IrO$_3$ stripyhoneycomb lattice. Experimentally measured magnetic susceptibilities suggest that Kitaev interactions, predicted for the ideal 90$^circ$ Ir-O-Ir bonds, are sizable in these materials. We first consider pure Kitaev interactions, which lead to an exactly soluble 3D quantum spin liquid (QSL) with emergent Majorana fermions and Z$_2$ flux loops. Unlike 2D QSLs, the 3D QSL is stable to finite temperature, with $T_c approx |K|/100$. On including Heisenberg couplings, exact solubility is lost. However, by noting that the shortest closed loop $ell$ is relatively large in these structures, we construct an $ellrightarrow infty$ approximation by defining the model on the Bethe lattice. The phase diagram of the Kitaev-Heisenberg model on this lattice is obtained directly in the thermodynamic limit, using tensor network states and the infinite-system time-evolving-block-decimation (iTEBD) algorithm. Both magnetically ordered and gapped QSL phases are found, the latter being identified by an entanglement fingerprint.
The Kitaev-Heisenberg (KH) model has been proposed to capture magnetic interactions in iridate Mott insulators on the honeycomb lattice. We show that analogous interactions arise in many other geometries built from edge-sharing IrO_6 octahedra, inclu
ding the pyrochlore and hyperkagome lattices relevant to Ir2O4 and Na4Ir3O8 respectively. The Kitaev spin liquid exact solution does not generalize to these lattices. However, a different exactly soluble point of the honeycomb lattice KH model, obtained by a four-sublattice transformation to a ferromagnet, generalizes to all these lattices. A Klein four-group =Z2xZ2 structure is associated with this mapping (hence Klein duality). A finite lattice admits the duality if a simple geometrical condition is met. This duality predicts fluctuation free ordered states on these different 2D and 3D lattices, which are analogs of the honeycomb lattice KH stripy order. This result is used in conjunction with a semiclassical Luttinger-Tisza approximation to obtain phase diagrams for KH models on the different lattices. We also discuss a Majorana fermion based mean field theory at the Kitaev point, which is exact on the honeycomb lattice, for the KH models on the different lattices. We attribute the rich behavior of these models to the interplay of geometric frustration and frustration induced by spin-orbit coupling.
Within the Landau paradigm, phases of matter are distinguished by spontaneous symmetry breaking. Implicit here is the assumption that a completely symmetric state exists: a paramagnet. At zero temperature such quantum featureless insulators may be fo
rbidden, triggering either conventional order or topological order with fractionalized excitations. Such is the case for interacting particles when the particle number per unit cell, f, is not an integer. But, can lattice symmetries forbid featureless insulators even at integer f? An especially relevant case is the honeycomb (graphene) lattice --- where free spinless fermions at f=1 (the two sites per unit cell mean f=1 is half filling per site) are always metallic. Here we present wave functions for bosons, and a related spin-singlet wave function for spinful electrons, on the f=1 honeycomb, and demonstrate via quantum to classical mappings that they do form featureless Mott insulators. The construction generalizes to symmorphic lattices at integer f in any dimension. Our results explicitly demonstrate that in this case, despite the absence of a non-interacting insulator at the same filling, lack of order at zero temperature does not imply fractionalization.
A Kitaev-Heisenberg-J2-J3 model is proposed to describe the Mott-insulating layered iridates A2IrO3 (A=Na,Li). The model is a combination of the Kitaev honeycomb model and the Heisenberg model with all three nearest neighbor couplings J1, J2 and J3.
A rich phase diagram is obtained at the classical level, including the experimentally suggested zigzag ordered phase; as well as the stripy phase, which extends from the Kitaev-Heisenberg limit to the J1-J2-J3 one. Combining the experimentally observed spin order with the optimal fitting to the uniform magnetic susceptibility data gives an estimate of possible parameter values, which in turn reaffirms the necessity of including both the Kitaev and farther neighbor couplings.
