Entanglement at strongly-interacting quantum critical points
Roger Melko University of Waterloo
PIRSA:13110071
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Unparticles and Fermi Arcs in the Cuprates
Philip Phillips University of Illinois Urbana-Champaign
PIRSA:13100131 -
Hofstadter’s Butterfly and interaction driven quantum Hall ferromagnetism in graphene
Philip Kim Columbia University
PIRSA:13110070 -
Staring into the Abyss
Avery Broderick University of Waterloo
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Fractional statistics in two-dimensions: Anyon there?
Smitha Vishveshwara University of Illinois Urbana-Champaign
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Z2 spin liquid in kagome Heisenberg antiferromagnet
Yuan Wan Chinese Academy of Sciences
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Induced Electroweak Symmetry Breaking and Supersymmetry
Jamison Galloway New York University (NYU)
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Feedback-regulated star formation on galactic and cosmological scales
Claude-André Faucher-Giguère University of California, Berkeley
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Entanglement at strongly-interacting quantum critical points
Roger Melko University of Waterloo
PIRSA:13110071At a quantum critical point (QCP) in two or more spatial dimensions, leading-order contributions to the scaling of entanglement entropy typically follow the "area" law, while sub-leading behavior contains universal physics. Different universal functions can be access through entangling subregions of different geometries. For example, for polygonal shaped subregions, quantum field theories have demonstrated that the sub-leading scaling is logarithmic, with a universal coefficient dependent on the number of vertices in the polygon. Although such universal quantities are routinely studied in non-interacting field theories, it requires numerical simulation to access them in interacting theories. In this talk, we discuss numerical calculations of the Renyi entropies at QCPs in 2D quantum lattice models. We calculate the universal coefficient of the vertex-induced logarithmic scaling term, and compare to non-interacting field theory calculations. Also, we examine the shape dependence of the Renyi entropy for finite-size lattices with smooth subregion boundaries. Such geometries provide a sensitive probe of the gapless wavefunction in the thermodynamic limit, and give new universal quantities that could be examined by field-theoretical studies in 2+1D. -
Unparticles and Fermi Arcs in the Cuprates
Philip Phillips University of Illinois Urbana-Champaign
PIRSA:13100131One of the open problems in strong correlation physics is whether or not Luttinger's theorem works for doped Mott insulators, particularly in the pseudo gap regime where the pole-like excitations form only a Fermi arc. I will begin this talk by using this theorem to count particles and show that it fails in general for the Mott state. The failure stems from the divergent self energy that underlies Mottness. When such a divergence is present, charged degrees of freedom are present that have no particle interpretation. I will argue that such excitations are governed by a non-trivial IR fixed point and the propagator of which is of the unparticle form proposed by Georgi. I will show how a gravity dual can be used to determine the scaling dimension of the unparticle propagator. I will close by elucidating a possible superconducting instability of unparticles and demonstrate that unparticle stuff is likely to display fractional statistics in the dimensionalities of interest for strongly correlated electron matter. Time permitting, an underlying theory of the strongly coupled fixed point will be outlined. -
Hofstadter’s Butterfly and interaction driven quantum Hall ferromagnetism in graphene
Philip Kim Columbia University
PIRSA:13110070Electrons moving in a periodic electric potential form Bloch energy bands where the mass of electrons are effectively changed. In a strong magnetic field, the cyclotron orbits of free electrons are quantized and Landau levels forms with a massive degeneracy within. In 1976, Hofstadter showed that for 2-dimensional electronic system, the intriguing interplay between these two quantization effects can lead into a self-similar fractal set of energy spectrum known as “Hofstadter’s Butterfly.” Experimental efforts to demonstrate this fascinating electron energy spectrum have continued ever since. Recent advent of graphene, where its Bloch electrons can be described by Dirac feremions, provides a new opportunity to investigate this half century old problem experimentally. In this presentation, I will discuss the experimental realization Hofstadter’s Butterfly via substrate engineered graphene under extremely high magnetic fields controlling two competing length scales governing Dirac-Bloch states and Landau orbits, respectively. In addition, the strong Coulomb interactions and approximate spin-pseudo spin symmetry are predicted to lead to a variety of integer quantum Hall ferromagnetic and fractional quantum Hall states and the quantum phase transition between them in graphene. I will discuss several recent experimental evidences to demonstrate the role of the electron interaction in single and bilayer graphene. -
Staring into the Abyss
Avery Broderick University of Waterloo
Nearly a century after their discovery, black holes remain one of the most striking, and problematic predictions of general relativity. Even more unsettling is the fact that they actually appear to exist! With only a handful of exceptions, every galaxy contains a supermassive behemoth, millions to billions as massive as the sun, at their center. These supermassive black holes are hardly incidental, they gravitationally power enormous outflows that rule the fates of their hosts. Despite the critical role they play in our understanding of gravity and impact upon the visible universe, actually testing their nature has remained beyond our reach - until now. Dr. Broderick will describe how astronomers are currently constructing (and operating) facilities that will image the horizons of black holes, and what we can already say about these enigmatic monsters in the dark. -
Fractional statistics in two-dimensions: Anyon there?
Smitha Vishveshwara University of Illinois Urbana-Champaign
A fascinating aspect of the two dimensional world is the possible existence of anyons, particles which obey 'fractional' statistics different from fermionic and bosonic statistics. In this colloquium, following an introduction to fractional particles in the context of quantum Hall systems, some of the tantalizing experiments for detecting the fractional charge of these particles will be described. Probes of fractional statistics in these systems will be discussed, drawing from analogies with the bosonic behavior of light studied by Hanbury Brown and Twiss in the 1950's as well as in the more recent beam-splitter settings in quantum optics. Finally, the exciting prospect of detecting fractional statistics in the context of superconductors will be explored. -
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A note on emergent classical behavior and approximations to decoherence functionals
Henrique Gomes University of Oxford
Although it can only be argued to have become consequential in the study of quantum cosmology, the question ``Why do we observe a classical world? " has been one of the biggest preoccupations of quantum foundations. In the consistent histories formalism, the question is shifted to an analysis of the telltale sign of quantum mechanics: superposition of states. In the consistent histories formalism, histories of the system which ``decohere", i.e. fall out of superposition or have negligible interference can be subjected to a notion of classical probability. In this paper we use an extension of Kirchoff's diffraction formula for wave functions on configuration spaces to give a different analysis and an approximation of decoherence. The Kirchoff diffraction formula lies conveniently at the midway between path integrals, wave equations, and classical behavior. By using it, we formulate an approximate dampening of the amplitude of superposition of histories. The dampening acts on each middle element of the fine-grained history {c_\alpha}, and is a function of the angle formed between {c_{n-1},c_n} and {c_n,c_{n+1}}, as classical trajectories in configuration space. As an example we apply the formalism to a modified gravity theory in the ADM gravitational conformal superspace. -
Z2 spin liquid in kagome Heisenberg antiferromagnet
Yuan Wan Chinese Academy of Sciences
A quantum spin liquid is a hypothesized ground state of a magnet without long-range magnetic order. Similar to a liquid, which is spatially uniform and strongly correlated, a quantum spin liquid preserves all the symmetries and exhibits strong correlations between spins. First proposed by P. W. Anderson in 1973, it has remained a conjecture until recently. In the past couple of years, numerical studies have provided strong evidences for quantum spin liquid in a simple model, the kagome Heisenberg antiferromagnet. In this talk, I will describe a low-energy effective theory for this magnet in terms of a lattice gauge theory with the simplest possible mathematical structure (a group of two elements, namely Z2). I will show that the theory reproduces many characteristic features observed numerically, thereby providing a bridge between the numeircs and the analytics. Furthermore, I will present theoretical predictions which could be tested in future numerical studies. -
From the symmetric group to giant gravitons in super Yang-Mills theory
In this talk we will discuss how giant gravitons and their open string interactions emerge from super Yang-Mills Theory. This is accomplished by diagonalizing the one loop dilatation operator on a class of operators with bare dimension of order N. From the result of this diagonalization, the Gauss Law governing the allowed open string excitations of giant gravitons is clearly visible. In addition, we show that this sector of the theory is integrable. -
Induced Electroweak Symmetry Breaking and Supersymmetry
Jamison Galloway New York University (NYU)
I'll discuss a class of supersymmetric models in which the physical Higgs mass is freed from the quartic coupling, thereby allowing for a 125 GeV Higgs state whose self-interaction can be much smaller than in the SM via a mechanism of 'induced EWSB'. This class of models provides a unique alternative to other realizations of natural SUSY, and the simplest realizations necessitate additional characteristic scalars below the TeV scale, thus altering phenomenological predictions for additional Higgses at the LHC. -
Feedback-regulated star formation on galactic and cosmological scales
Claude-André Faucher-Giguère University of California, Berkeley
A central problem in galaxy formation is to understand why star formation is so inefficient. Within individual galaxies, gas is converted into stars at a rate two orders of magnitude slower than unimpeded gravitational collapse predicts, a fact embodied in the low normalization of the observed Kennicutt-Schmidt (K-S) relationship between star formation rate surface density and gas surface density. Star formation in galaxies is also globally inefficient in the sense that the stellar mass in dark matter halos is a small fraction of the universal baryon fraction. I will show that these two facts can be explained by the self-regulation of star formation by feedback from massive stars. Within galaxies, stellar feedback drives turbulence that supports the interstellar medium against collapse and the K-S law is set by the low strength of gravity relative to stellar feedback. The energy input from the same stellar feedback processes drive powerful galactic outflows that remove most of the gas accreted from the intergalactic medium before it has time to turn into stars. Using cosmological hydrodynamical simulations from our FIRE project ("Feedback In Realistic Environments"), I will show that gas removal by star formation-driven galactic winds successfully explains the observed galaxy stellar mass function, at least for galaxies less massive than the Milky Way. Feedback from massive black holes may be required to explain the quenching of more massive galaxies. Motivated by recent observations, I will discuss the physics of galactic winds driven by active galactic nuclei. -