This series consists of talks in the area of Condensed Matter.
Holographic duality is a duality between quantum many-body systems (boundary) and gravity systems with one additional spatial dimension (bulk). In this talk, I will describe a new approach to holographic duality for lattice systems, called the exact holographic mapping. The key idea of this approach can be summarized by two points: 1) The bulk theory is nothing but the boundary theory viewed in a different basis. 2) Space-time geometry is determined by the structure of correlations and quantum entanglement in a quantum state.
A topological phase is a phase of matter which cannot be characterized by a local order parameter. We first introduce non-local order parameters that can detect symmetry protected topological (SPT) phases in 1D systems and then show how to generalize the idea to detect symmetry enriched topological (SET) phases in 2D. SET phases are new structures that occur in topologically ordered systems in the presence of symmetries. We introduce simple methods to detect the SET order directly from a complete set of topologically degenerate ground state wave functions.
The talk is divided into two parts: in the first, I will talk about dynamics of far-from equilibrium initial states in different lattice models. I will present results of quench dynamics of the XXZ-Heisenberg magnet, where interesting physics emerges after quenching the system. Then I will present results for scattering of solitonic objects in different integrable and non-integrable lattice models. In the second part, I will talk about dynamics of impurity systems.
The quantum spin liquid is an emergent new state of matter, which has attracted a lot of recent attention. In particular, the time reversal symmetry broken spin liquid (Kalmeyer et. al. and Wen et. al.), characterized by the chiral ordering and fractionalized quasi-particle as a realization of the fractional quantum Hall state had been proposed for more than 20 years, but never identified as the true ground state in any more generic (e.g. Heisenberg spin exchange) models with time reversal symmetry.
What is the price of naturalness? In minimal extensions of the standard model, stringent limits on new colored particles and measurements of Higgs properties from the LHC severely challenge the hypothesis of naturalness of the electroweak scale. However, these measurements also provide unprecedented guidance in exploring non-minimal models of new electroweak physics.
A non-perturbative definition of anomaly-free chiral fermions and bosons in 1+1D spacetime as finite quantum systems on 1D lattice is proposed. In particular, any 1+1D anomaly-free chiral matter theory can be defined as finite quantum systems on 1D lattice with on-site symmetry, if we include strong interactions between matter fields. Our approach provides another way, apart from Ginsparg-Wilson fermions approach, to avoid the fermion-doubling challenge.
Quantum spin liquid (QSL) is an exotic phase of matter and provides an interesting example of emergent non-locality. Even though many materials have been proposed as candidates for QSLs, there is no direct confirmation of QSLs in any of these systems. Quantum spin ice (QSI) is a physical realization of U(1) QSLs on the pyrochlore lattice. We consider a class of electron systems in which dipolar-octupolar Kramers doublets arise on the pyrochlore lattice. In the localized limit, the Kramers doublets are described by the effective spin 1/2 pseudospins.
The amplitude mode is a ubiquitous phenomenon in systems with broken continuous symmetry and effective relativistic dynamics, and has been observed in magnets, charge density waves, cold atom systems, and superconductors. It is a simple analog of the Higgs boson of particle physics. I will discuss the properties of the amplitude mode and its somewhat surprising visibility in two-dimensional systems, recently confirmed in cold atom experiments.
In the study of strongly-correlated insulators, a long-standing puzzle remained open for over 40 years. Some Kondo insulators (or mixed-valent insulators) display strange electrical transport that cannot be understood if one assumes that it is governed by the three-dimensional bulk. In this talk, I show that some 3D Kondo insulators have the right ingredients to be topological insulators, which we called “topological Kondo insulators”.