Emergence in Complex Systems
A 3d electron topological insulator (ETI) is a phase of matter protected by particle-number conservation and time-reversal symmetry. It was previously believed that the surface of an ETI must be gapless unless one of these symmetries is broken. A well-known symmetry-preserving, gapless surface termination of an ETI supports an odd number of Dirac cones. In this talk, I will show that in the presence of strong interactions, an ETI surface can actually be gapped and symmetry preserving, at the cost of carrying an intrinsic two-dimensional topological order.
In both classical and quantum critical systems, universal contributions to the mutual information and Renyi entropy depend on geometry. I will first explain how in 2d classical critical systems on a rectangle, the mutual information depends on the central charge in a fashion making its numerical extraction easy, as in 1d quantum systems. I then describe analogous results for 2d quantum critical systems. Specifically, in special 2d quantum systems such as quantum dimer/Lifshitz models, the leading geometry-dependent term in the Renyi entropies can be computed exactly.
We demonstrate that the many-body localized phase is characterized by the existence of infinitely many local conservation laws. We argue that many-body eigenstates can be obtained from product states by a sequence of nearly local unitary transformation, and therefore have an area-law entanglement entropy, typical of ground states. Using this property, we construct the local integrals of motion in terms of projectors onto certain linear combinations of eigenstates .
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.
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.
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.
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.
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
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.
Symmetry protected topological (SPT) states are generalizations of topological band insulators to interacting systems. They possess a gapped bulk spectrum together with symmetry protected edge states, with no topological order. There has been recently an intense effort to classify SPT states both in terms of group cohomology as well as from the point of view of effective field theories. An interesting related question is to understand the structute of lattice models that realize SPT physics.