June 9: Xiaoling Qi (UCSB/Stanford)
I will give an informal review of topological insulators and topological superconductors.
(1). In the first talk I will introduce the theoretical models, general effective field theory and physical properties of topological insulators. I will also briefly review the current experimental situation.
(2) In the second talk I will review the generalization of topological insulators to most generic symmetry classes and dimensions. Then I will focus on chiral topological superconductors and its relation to Majorana fermions and topological quantum computation.
June 10: Zheng-Cheng Gu (UCSB)
1) Grassman tensor network approach to strongly correlated system
2) Wave function renormalization and topological order
June 11: Hong Yao (Berkeley)
1) Composite Fermion Liquids and Quantum Hall Stripes on the Topological Insulator Surface: We study the problem of a single Dirac fermion, which can be realized on the surface of a topological insulator, in a quantizing orbital magnetic field, when the chemical potential is at the Dirac point. With both long-range Coulomb repulsion and short-range local repulsion, we obtain its phase diagram. Exotic phases, such as composite Fermi liquids and quantum Hall stripes, are predicted to occur under appropriate conditions.
2) Topological insulators and topological non-linear sigma models We link the physics of topological non-linear sigma models with that of Chern-Simons insulators. We show that corresponding to every 2n-dimensional Chern-Simons insulator there is a (n-1)-dimensional topological non-linear sigma model with the Wess-Zumino-Witten term. Breaking internal symmetry in these non-linear sigma models leads to non-linear sigma models with the theta term.
June 13: Xie Chen (MIT)
Title: Wavefunction Renormalization of Tensor Product States and Classification of Topological Order
Abstract: Two gapped quantum ground states in the same phase are connected by an adiabatic evolution which gives rise to a local unitary transformation that maps between the states. Therefore, local unitary transformations define an equivalence relation among states in the same universality class of a gapped quantum phase, hence with the same topological order. Based on the tensor product representation of quantum ground states, we give an explicit construction of a specific local unitary transformation which performs wave function renormalization and flows a wavefunction to a simpler form within the same equivalence/universality class. The fixed point under this renormalization scheme gives a classification of topological order. First, we discuss the situation in 1D spin chains and show that there is no topological order in 1D, i.e. every state can be mapped to product states with local unitary transformations. Further, we classify all possible phases in 1D spin chains when certain symmetry is required for the system. Next, we will show how such a renormalization procedure can be carried out in 2D and demonstrate some examples where it can be used to identify phase transition points, for both topological and symmetry breaking phases.
June 17: Antonio Miguel Garcia-Garcia (Technical University of Lisbon)
Talk I:Finite size effects in superconducting nanograins: from theory to experiments:
The first part of the talk is devoted to a theoretical description of finite size effects in Bardeen Cooper Schrieffer (BCS) superconductors. Then we study superconductivity in single isolated Pb and Sn nanoparticles. In Sn nanoparticles we observe giant oscillations in the superconducting energy gap with particle size leading to enhancements as large as 60%. Contrarily, we observe no such oscillations in the gap for Pb nanoparticles, which is ascribed to the suppression of shell effects for shorter coherence lengths. Theoretically, these finite size effects are described quantitatively by introducing finite-size corrections to BCS model. For Pb grains we have also observed that, at low temperatures, the superconducting gap diminishes as the grain size is reduced. By contrast, for sufficiently small grains, the gap is finite even for temperatures higher than then the mean field critical temperature. A model including thermal fluctuations and the leading low temperature corrections to mean field provides a quantitative description of the system. Our study paves the way to exploit quantum size effects in boosting superconductivity in nanograins. Finally, motivated by recent advances in high energy physics and cold atom we explore novel forms of pairing and superconductivity in strongly interacting systems.
Talk II:Recent developments in Anderson Localization: from fundamental aspects to applications in cold atoms and quantum chromodynamics:
In the first part of the talk I introduce the phenomenon of Anderson localization and discuss recent theoretical approaches to describe the metal insulator transition. In the second part I describe the role of Anderson localization in the chiral phase transition that occurs in QCD at finite temperature. Motivated by recent experiments in cold atoms I investigate the interplay of disorder and interactions in 1d Fermi gases and the conditions under which Anderson localization is suppressed in 1d disordered systems.
June 18:Cenke Xu (Harvard/UCSB)
Title:Introduction to Quantum Criticality
Abstract:We will discuss several interesting subjects related to quantum criticality, in a nontechnical manner. We will start with a review of scaling and renormalization group, and then apply scaling and power-counting argument to practical situations, such as Harris criterion, phase transition in Fermi liquid, phase transition in superfluid, hyperscaing and dangerously irrelevant operators, classical phase transitions with effective dynamical scaling et.al. Then we will discuss the duality transformation and mapping between different quantum critical points in modeled systems.
June 22: Kun Yang (Florida State University)
Talk I:Probing non-Abelian Quasiparticles at the Edge and in the Bulk of Quantum Hall Liquids
Fractional quantum Hall (FQH) systems are among the most intriguing many-particle systems known to physicists, with extremely rich internal structure. One of their most exotic properties is that they support fractionally charged quasiparticles with fractional statistics. Recently there has been very strong interest in the so-called non-Abelian FQH liquids, in which their quasiparticle statistics is non-Abelian, in that the ground state degeneracy of the system grows exponentially with quasiparticle number, and these ground states form non-Abelian representations of the braiding group. Experimental evidence of such exotic statistics remains elusive, but some encouraging progress has been made recently. In this talk we will discuss how one can reveal the non-Abelian statistics experimentally, by probing the FQH liquid in the bulk or at the edge. We showed that bulk thermopower is a promising way to detect the non-Abelian nature, and measure the quantum dimension (a key parameter that quantifies non-Abelian statistics) of these quasiparticles. We also demonstrated a novel cooling effect for such quasiparticles. For the specific candidate system of FQH liquid at filling factor 5/2, we performed numerical calculations that allow for quantitative comparison between theory and on-going edge interference experiments. In particular, we proposed to distinguish the two leading theoretical candidate states, Moore-Read Pfaffian and anti-Pfaffian, using momentum-resolved electron tunneling into the edge, as they have very different edge electron spectral functions.
Talk II:Novel Quantum Criticality and Emergent Particles in Trapped Cold Atom Systems
Trapped cold atoms systems have emerged as a new frontier of research in condensed matter physics. In particular, physics associated with strong interaction/correlation in such systems is of strong current interest. In this talk I will describe several examples in which quantum phase transitions and emergent particles with exotic properties arise in such systems, which do not have counter parts in traditional electronic condensed matter systems. These include: (i) a transition from an integer quantum Hall phase to a fractional quantum Hall phase where the critical theory is that of a massless relativistic semion; (ii) new universality class of superfluid-insulator transition in Bose-Fermi mixtures, and high-Tc p-wave fermion pairing mediated by quantum critical fluctuations; and (iii) the possibility of realizing supersymmetry in Bose-Fermi mixtures, and detecting a Goldstone fermion called Goldstino in such systems.
June 25:
9:30-10:45 Talk I by Shi-Zhong Zhang (Ohio-State University) : BEC-BCS crossover
We discuss some general observations on the BEC-BCS crossover problem, as currently implemented with the ultracold Fermi alkali gases. It is shown that some of the specific properties of the dilute Fermi gas allows a theoretical simplification which is not possible in other systems where crossover are discussed. We also mention some recent developments and experimental confirmation of those considerations.
10:45-12:00 Talk II by Kai Wu( Tsinghua ): Curie-Weiss-metal state in overdoped cobaltates
We present the discovery of a new state of electron matter that descends from a strongly interacting microscopy described by a t-J model on a triangular lattice where due to the altered role of quantum statistics the spin degrees of freedom localize in 'statistical' Landau orbits, while the charge carriers form a bose metal that feels the spins through random gauge fields. In sharp contrast to the Fermi-liquid saddle-point state, this extraordinary new state exhibits quite different low-energy properties including Curie-Weiss magnetic susceptibility, large thermopower, and linear-temperature resistivity. It indicates that the Mott physics remains important at high-doping. Comparison with the experimental measurements in the \textrm{Na}$_{x}$\textrm{CoO}$_{2}$ system at $x>0.5$ is made and also a 'smoking gun' structure in neutron scattering is predicted. This new state provide a possible new route to seeking efficient thermoelectric material.
2:30-3:45 Talk III by Wei-Qiang Chen( Hong-Kong University): Strong coupling theory and pairing state of iron pnictide superconductor
Superconductivity in iron pnictides is studied by using a two-orbital Hubbard model in the large U limit. The inter-pocket pair scatterings determine the symmetry of the superconductivity, which is $s_\pm$ at small Hund's couplings and d-wave at large Hund's rule coupling and large U. The phase sensitive experiment is also discussed for detecting the $s_\pm$ symmetry.
3:45-5:00 Talk IV by Peng Ye( Tsinghua): What happens in zero-temperature underdoped Mott insulators?
Starting from phase-string representation of t-J model, we construct a quantum field theory defined on lattice, namely, ``compact mutual Chern-Simons theory''. We show that in underdoped Mott insulators, at zero temperature, the phase diagram is characterized by unconventional "order parameters"--a pair of Wilson loops. At phase boundaries, they display non-analyticity in the dopant concentration, signaling non-Landau-Ginzburg-Wilson type quantum phase transitions. Specifically, as the doping level increases, the system undergoes Antiferromagnetic phase (AF), Bose insulating phase (BI) and Superconducting phase (SC). These phases are well characterized by the Wilson loops and their linear response theoretical description is fully determined by a new composition rule of electric conductivity in terms of spin-charge separated contributions (i.e. the physical electric conductivity is a function of holon conductivity and spinon conductivity, in which, spinon carries spin while holon carries charge). Most strikingly, the intermediate BI phase shows its very feature that both of spin and charge degrees of freedom exist as deconfined degrees of freedom. Note that, in AF (SC) phase, spin (charge) is deconfined, while charge (spin) is confined. Apart from these results, we also obtain the quantitative relations between the photon mass (spin stiffness) and spin gap (charge gap) in SC (AF) phase. All of these results, as well as the other phenomena (such as magnetic flux quantization at hc/(2e), uniform magnetic susceptibility etc.) are actually deeply rooted in the topological term-Mutual Chern-Simons term.
