This series consists of talks in the area of Condensed Matter.
The evolution of many kinetic processes in 1+1 dimensions results in 2D directed percolative landscapes. The active phases of those models possess numerous hidden geometric orders characterized by distinct percolative patterns. From Monte-Carlo simulations of the directed percolation (DP) and the contact process (CP) we demonstrate the emergence of those patterns at specific critical points as a result of continuous phase transitions.These geometric transitions belong to the DP universality class and their nonlocal order parameters are the capacities of corresponding backbones.
The condensation of bosons can induce transitions between topological quantum field theories (TQFTs). This as been previously investigated through the formalism of Frobenius algebras and with the use of Vertex lifting coefficients. I will discuss an alternative, algebraic approach to boson condensation in TQFTs that is physically motivated and computationally efficient.
In this talk, I will revise some of the aspects that lead isolated interacting quantum systems to thermalize.
In the presence of disorder, however, the thermalization process fails resulting in a phenomena where
transport is suppressed known as many-body localization. Unlike the standard Anderson localization for
non-interacting systems, the delocalized (ergodic) phase is very robust against disorder even for moderate
values of interaction. Another interesting aspect of the many-body localization phase is that under the time
Topological aspects of physical systems, including the called topological states of matter, have become hot topics in the frontiers of physics in recent years. Here I would like to present a mathematically "popular" talk for professional physicists for a highlight or overview of how one can systematize knowledge of topological aspects of quantum field theories. Our starting points are Descent Equations and Gauge Structure in Configuration Space in Field Theory. (The audience needs only to know the meaning of "differential forms".)
The orbital angular momentum in a chiral superfluid has posed a paradox for several decades. For example, for the $p+ip$-wave superfluid of $N$ fermions, the total orbital angular momentum should be $N/2$ if all the fermions form Cooper pairs. On the other hand, it appears to be substantially suppressed from $N/2$, considering that only the fermions near the Fermi surface would be affected by the pairing interaction. To resolve the long-standing question, we studied chiral superfluids in a two-dimensional circular well, in terms of a conserved charge and spectral flows.
Matrix product operators form a natural language for describing topological quantum order. I will discuss how they arise as symmetries in PEPS, how anyon excitations arise as end points on them, and how the virtual indices of the MPO's provide a tensor product structure for the logical qubits in topological quantum computation.
Using the method of flux fusion anomaly test recently developed by M. Hermele and X. Chen (arXiv:1508.00573), we show that the possible ways of fractionalize crystal symmetry is greatly restricted if we assume the spin liquid has an SU(2) spin rotation symmetry and the spinon carries a half-integer spin. For a Z_2 spin liquid, under these assumptions the vison can only take the crystal symmetry fractionalization described by the Ising gauge theory. For a chiral spin liquid these assumptions imply that the spinon must also take fractionalized quantum numbers of crystal symmetries.
In this talk, we will analyze the properties of the bosonic $\nu = 1$ Moore-Read state when used to build a state
which is strongly believed to be a non-Abelian spin-1 chiral spin liquid state . In this state the bosonic $\nu = 1$
A pedagogic introduction will be given to: i) Emergent Majorana fermions and Majorana zero modes in certain condensed matter models and ii) Kondo insulators. This will be followed by discussion of a remarkable Quantum Oscillation Anomaly seen in recent experiments in SmB6, a Kondo insulator, by the Cambridge group , as providing evidence  for presence of Majorana fermi sea, in an unexpected place. We show a counter intuitive result that these Majorana fermions though neutral, exhibit Landau diamagnetism.