Chiral topological insulator of magnons

We propose a magnon realization of 3D topological insulator in the AIII (chiral symmetry) topological class. The topological magnon gap opens due to the presence of Dzyaloshinskii-Moriya interactions. The existence of the topological invariant is established by calculating the bulk winding number of the system. Within our model, the surface magnon Dirac cone is protected by the sublattice chiral symmetry. By analyzing the magnon surface modes, we confirm that the backscattering is prohibited. By weakly breaking the chiral symmetry, we observe the magnon Hall response on the surface due to opening of the gap. Finally, we show that by changing certain parameters the system can be tuned between the chiral topological insulator (mcTI), three dimensional magnon anomalous Hall (3D-mAH), and Weyl magnon phases.Comment: 6 page

Spin Hall and Nernst effects of Weyl magnons

In this paper, we present a simple model of a three-dimensional insulating magnetic structure which represents a magnonic analog of the layered electronic system described in [Phys. Rev. Lett. {\bf 107}, 127205 (2011)]. In particular, our model realizes Weyl magnons as well as surface states with a Dirac spectrum. In this model, the Dzyaloshinskii-Moriya interaction is responsible for the separation of opposite Weyl points in momentum space. We calculate the intrinsic (due to the Berry curvature) transport properties of Weyl and so-called anomalous Hall effect (AHE) magnons. The results are compared with fermionic analogs.Comment: 9 pages, 5 figures, published versio

Theory of magnon motive force in chiral ferromagnets

We predict that magnon motive force can lead to temperature dependent, nonlinear chiral damping in both conducting and insulating ferromagnets. We estimate that this damping can significantly influence the motion of skyrmions and domain walls at finite temperatures. We also find that in systems with low Gilbert damping moving chiral magnetic textures and resulting magnon motive forces can induce large spin and energy currents in the transverse direction

Magnon spin Nernst effect in antiferromagnets

We predict that a temperature gradient can induce a magnon-mediated spin Hall response in an antiferromagnet with non-trivial magnon Berry curvature. We develop a linear response theory which gives a general condition for a Hall current to be well defined, even when the thermal Hall response is forbidden by symmetry. We apply our theory to a honeycomb lattice antiferromagnet and discuss a role of magnon edge states in a finite geometry.Comment: 17 page

Spin glass reflection of the decoding transition for quantum error correcting codes

We study the decoding transition for quantum error correcting codes with the help of a mapping to random-bond Wegner spin models. Families of quantum low density parity-check (LDPC) codes with a finite decoding threshold lead to both known models (e.g., random bond Ising and random plaquette $\Z2$ gauge models) as well as unexplored earlier generally non-local disordered spin models with non-trivial phase diagrams. The decoding transition corresponds to a transition from the ordered phase by proliferation of extended defects which generalize the notion of domain walls to non-local spin models. In recently discovered quantum LDPC code families with finite rates the number of distinct classes of such extended defects is exponentially large, corresponding to extensive ground state entropy of these codes. Here, the transition can be driven by the entropy of the extended defects, a mechanism distinct from that in the local spin models where the number of defect types (domain walls) is always finite.Comment: 15 pages, 2 figure

Fault-Tolerance of "Bad" Quantum Low-Density Parity Check Codes

We discuss error-correction properties for families of quantum low-density parity check (LDPC) codes with relative distance that tends to zero in the limit of large blocklength. In particular, we show that any family of LDPC codes, quantum or classical, where distance scales as a positive power of the block length, $d \propto n^\alpha$, $\alpha>0$, can correct all errors with certainty if the error rate per (qu)bit is sufficiently small. We specifically analyze the case of LDPC version of the quantum hypergraph-product codes recently suggested by Tillich and Z\'emor. These codes are a finite-rate generalization of the toric codes, and, for sufficiently large quantum computers, offer an advantage over the toric codes.Comment: 4.5 pages, 1 figur

Hybrid skew scattering regime of the anomalous Hall effect in Rashba systems: unifying Keldysh, Boltzmann, and Kubo formalisms

We present the analytical description of the anomalous Hall effect (AHE) in a 2DEG ferromagnet within the Keldysh formalism. These results unify all three linear response approaches to anomalous Hall transport and close a long standing debate. We are able to identify a new extrinsic AHE regime dominated by a hybrid skew scattering mechanism. This new contribution is inversely proportional to the impurity concentration, resembling the normal skew scattering, {\em but} independent of the impurity-strength, resembling the side-jump mechanism. Within the Kubo formalism this regime is captured by higher order diagrams which, although weak, dominate when both subbands are occupied; this regime can be detected by variable remote doping experiments that we describe.Comment: 5 pages, 2 figure