In this talk, I will show the emergence of p+ip topological superconducting ground state in infinite-U Hubbard model on honeycomb lattice, from both state-of-art Grassmann tensor-network numerical approach and quantum field theory approach.
Some time ago (1999), Dy2Ti2O7, was shown to be a magnetic analog of water ice, and thus dubbed "spin ice". Recently, theories and experiments have developed the perspective of viewing excitations within the low temperature phase of this spin ice as monopoles. I will present early results of specific heat, ac susceptibility and magnetization measurements as well as my group's recent results on this system
Standard picture of a topologically-nontrivial phase of matter is an insulator with a bulk energy gap, but metallic surface states, protected by the bulk gap. Recent work has shown, however, that certain gapless systems may also be topologically nontrivial, in a precise and experimentally observable way. In this talk I will review our work on a class of such systems, in which the nontrivial topological properties arise from the existence of nondegenerate point band-touching nodes (Weyl nodes) in their electronic structure. Weyl nodes generally exist in any three-dimensional material with a broken time-reversal or inversion symmetry. Their effect is particularly striking, however, when the nodes coincide with the Fermi energy and no other states at the Fermi energy exist. Such "Weyl semimetals" have vanishing bulk density of states, but have gapless metallic surface states with an open (unlike in a regular two-dimensional metal) Fermi surface ("Fermi arc"). I will discuss our proposal to realize Weyl semimetal state in a heterostructure, consisting of alternating layers of topological and ordinary insulator, doped with magnetic impurities. I will further show that, apart from Weyl semimetals, even such "ordinary" materials as common metallic ferromagnets, in fact also possess Weyl nodes in the electronic structure, leading to the appearance of chiral Fermi-arc surface states and the corresponding contribution to their intrinsic anomalous Hall conductivity.
After a short introduction to open inflation and the observed large-scale cosmic microwave anomalies, which have been confirmed by the Planck satellite, I'll argue that the anomalies are naturally explained in the context of a marginally-open, negatively curved universe. I'll look in particular at the dipole power asymmetry, and motivate that this asymmetry can happen if our universe has bubble nucleated in a phase transition during a period of early inflation, and, as a result, has open geometry. Open inflation models, which are motivated by the string landscape and can excite `super-curvature' perturbation modes, can explain the presence of a very-large-scale perturbation, like the one we observe, which leads to a dipole modulation of the power spectrum. I'll provide a specific implementation of the scenario which is compatible with all existing constraints.
We show that double perovskites with 3d and 5d transition metal ions exhibit spin-orbit coupled magnetic excitations, finding good agreement with neutron scattering experiments in bulk powder samples. Motivated by experimental developments in the field of oxide heterostructures, we also study double perovskites films grown along the  direction. We show that spin-orbit coupling in such low dimensional systems can drive ferromagnetic order due to electronic correlations. This results in topological Chern bands, with symmetry-allowed trigonal deformations leading to quantum anomalous Hall states supporting a pair of chiral edge modes.
We developed a general method to compute the correlation functions of FQH states on a curved space. The computation features the gravitational trace anomaly and reveals geometric properties of FQHE. Also we highlight a relation between the gravitational and electromagnetic response functions. The talk is based on the recent paper with T. Can and M. Laskin.
I will look at two cases of the interplay of geometry (curvature) and topology: (1) 3D Topological metals: how to understand their surface "Fermi arcs" in terms of their emergent conservation laws and the Streda formula for the non-quantized anomalous Hall effect. (2) The Hall viscosity tensor in the FQHE as a local field, and its Gaussian-curvature response that allows local compression or expansion of the fluid to accommodate substrate inhomogeneity.