This series consists of talks in the area of Condensed Matter.
Parafermions are the simplest generalizations of Majorana fermions that realize topological order. We propose a less restrictive notion of topological order in 1D open chains, which generalizes the seminal work by Fendley [J. Stat. Mech., P11020 (2012)]. The first essential property is that the groundstates are mutually indistinguishable by local, symmetric probes, and the second is a generalized notion of zero edge modes which cyclically permute the groundstates.
The standard theory of topological insulators and superfluids (or superconductors) assumes that the fermionic elementary excitations in these systems – electrons in the insulator and Bogoliubov quasiparticles in the superfluid – do not interact with one another. In this talk I will discuss extensions of this theory to include the effects of interparticle interactions on the topological surface states of 3D topological insulators and superfluids.
Recent progress on the construction of holographic lattices and its applications to AdS/CMT correspondence will be briefly reviewed. Our special interests will focus on the building of bulk geometry of gravity whose holographic duals exhibit metal-insulator transitions (MIT). In particular, the Peierls phase transition induced by charge density waves is implemented in a holographic manner. The holographic entanglement entropy close to quantum critical points will be discussed as well.
Symmetry-protected topological (SPT) phases can be thought of as generalizations of topological insulators. Just as topological insulators have robust boundary modes protected by time reversal and charge conservation symmetry, SPT phases have boundary modes protected by more general symmetries. In this talk, I will describe a method for analyzing 2D and 3D SPT phases using braiding statistics. More specifically, I will show that 2D and 3D SPT phases can be characterized by gauging their symmetries and studying the braiding statistics of their gauge flux excitations.
I will show how hydrodynamics is modified if the underlying fluid constituents are massless Weyl fermions, which are anomalous at the quantum level. Because of the nondissipative nature of the modification I will construct a partition function which compactly describes the transport properties of the system and I will explain how the anomalous properties can be understood in terms of kinetic theory and heat kernels.
We examine the interplay of symmetry and topological order in 2+1D topological phases of matter. We define the topological symmetry group, characterizing symmetry of the emergent topological quantum numbers, and describe its relation with the microscopic symmetry of the physical system.
Does a generic quantum system necessarily thermalize? Recent developments in disordered many-body quantum systems have provided crucial insights into this long-standing question. It has been found that sufficiently disordered systems may fail to thermalize leading to a 'many-body localized' phase. In this phase, the fundamental assumption underlying equilibrium statistical mechanics, namely, the equal likelihood for all states at the same energy, breaks down.
Holographic duality is a duality between gravitational systems and non-gravitational systems. In this talk, I will propose a different approach for understanding holographic duality named as the exact holographic mapping. The key idea of this approach can be summarized by two points: 1) The bulk theory and boundary theory are related by a unitary mapping in the Hilbert space. 2) Space-time geometry is determined by the structure of correlations and quantum entanglement in a quantum state. When applied to lattice systems, the holographic mapping is defined by a unitary tensor network.