This series consists of talks in the area of Condensed Matter.
The entanglement spectrum denotes the eigenvalues of the reduced density matrix of a region in the ground state of a many-body system. Given these eigenvalues, one can compute the entanglement entropy of the region, but the full spectrum contains much more information. I will review geometric methods to extract this spectrum for special subregions in lorentz and conformally invariant field theories (and any theory whose universal low energy physics is captured by such a field theory).
Rare earth pyrochlores, with a chemical formula A2B2O7, exhibit many interesting features in A site spin system. Depending on A site rare earth elements, spin ice and magnetically ordered phases are shown in several experiments. Moreover, they have been also focused as possible candidates of U(1) spin liquid. In order to explore such versatile phases, we study the pseudospin-1/2 model, which is quite generic to describe rare earth pyrochlores with integer spins, in the presence of spin-orbit coupling and crystalline electric field.
Novel phases can result from the interplay of electronic interactions and spin orbit coupling. In the first part, we discuss a simple Hubbard model for the pyrochlore iridates, whose phase diagram contains topological insulator (TI) and various magnetic phases. The latter host the novel topological Weyl semimetal, whose excitations behave like Weyl fermions. In the second part we study a novel spin liquid that was proposed to arise in the iridates, the 3D topological Mott insulator: a fractionalized TI where the neutral spinons acquire a topologically non-trivial band structure.
A fractional quantized Hall nematic (FQHN) is a novel phase in which a fractional quantum Hall conductance coexists with broken rotational symmetry characteristic of a nematic. Both the topological and symmetry-breaking order present are essential for the description of the state, e..g, in terms of transport properties. Remarkably, such a state has recently been observed by Xia et al. (cond-mat/1109.3219) in a quantum Hall sample at 7/3 filling fraction.
Recent years have seen a renewed interest, both theoretically and experimentally, in the search for topological states of matter. On the theoretical side, while much progress has been achieved in providing a general classification of non-interacting topological states, the fate of these phases in the presence of strong interactions remains an open question. The purpose of this talk is to describe recent developments on this front.
The multiscale entanglement renormalization ansatz can be reformulated in terms of a causality constraint on discrete quantum dynamics. This causal structure is that of de Sitter space with a flat spacelike boundary, where the volume of a spacetime region corresponds to the number of variational parameters it contains.
We consider the effect of an in-plane current on the magnetization dynamics of a quasi-two-dimensional spin-orbit coupled nanoscale itinerant ferromagnet. By solving the appropriate kinetic equation for an itinerant electron ferromagnet, we show that Rashba spin-orbit interaction provides transport currents with a switching action, as observed in a recent experiment (I. M.
Miron et al., Nature 476, 189 (2011)). The dependence of the effective switching field on the magnitude and direction of an external magnetic field in our theory agrees well with experiment.
Many-body entanglement, the special quantum correlation that exists among a large number of quantum particles, underlies interesting topics in both condensed matter and quantum information theory. On the one hand, many-body entanglement is essential for the existence of topological order in condensed matter systems and understanding many-body entanglement provides a promising approach to understand in general what topological orders exist.
I will describe our recent work on a new topological phase of matter: topological Weyl semimetal. This phase arises in three-dimensional (3D) materials, which are close to a critical point between an ordinary and a topological insulator. Breaking time-reversal symmetry in such materials, for example by doping with sufficient amount of magnetic impurities, leads to the formation of a Weyl semimetal phase, with two (or more) 3D Dirac nodes, separated in momentum space.