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< 2020 >
  • CMSA EVENT: CMSA Condensed Matter/Math Seminar: Deconfined metallic quantum criticality-I
    9:00 AM-10:30 AM
    July 9, 2020

    A number of strongly correlated electronic materials exhibit quantum criticality that does not fit into the conventional Landau-Ginzburg-Wilson paradigm of continuous phase transitions. Inspired by these experimental examples, I will discuss a new class of quantum phase transitions that describe a continuous transition between a Fermi liquid metal with a generic electronic Fermi surface and electrical insulators without Fermi surface of neutral excitations. Such phase transitions are described in terms of a finite density of fractionalized excitations coupled to emergent gauge fields. I will discuss various concrete examples of such gauge theories and describe their associated phase transitions using a renormalization group framework.  Remarkably, we find examples of continuous phase transitions between Landau Fermi liquid metals and insulators, where the quantum critical point hosts a non-Fermi liquid with a sharp Fermi surface but no long-lived quasiparticles. I will comment on the relevance of this new theoretical framework for some of the most pressing questions in the field of quantum matter.



    Integrability and Braided Tensor Categories

    10:00 AM-11:00 AM
    July 14, 2020

    Many integrable critical classical statistical mechanical models and the corresponding quantum spin chains possess a fractional-spin conserved current. Such currents have been constructed by utilizing quantum-group algebras, fermionic and parafermionic operators, and ideas from “discrete holomorphicity”. I define them generally and naturally using a braided tensor category, a topological structure familiar from the study of knot invariants, anyons and conformal field theory.  I derive simple constraints on the Boltzmann weights necessary and sufficient for such a current to exist, generalizing those found using quantum-group algebras. I find many solutions, in both geometric and local models. In all cases, the resulting weights are those of an integrable lattice model, giving a linear construction for “Baxterising”, i.e. building a solution of the Yang-Baxter equation out of topological data.


  • CMSA EVENT: CMSA Condensed Matter/Math Seminar: Deconfined metallic quantum criticality – II
    10:30 AM-12:00 PM
    July 16, 2020

    The main goal of this talk is to discuss in detail a concrete setup for deconfined metallic quantum criticality. In particular, we propose that certain quantum Hall bilayers can host examples of a deconfined metal-insulator transition (DMIT), where a Fermi liquid (FL) metal with a generic electronic Fermi surface evolves into a gapped insulator (or, an insulator with Goldstone modes) through a continuous quantum phase transition. The transition can be accessed by tuning a single parameter, and its universal critical properties can be understood using a controlled framework. At the transition, the two layers are effectively decoupled, where each layer undergoes a continuous transition from a FL to a generalized composite Fermi liquid (gCFL). The thermodynamic and transport properties of the gCFL are similar to the usual CFL, while its spectral properties are qualitatively different. The FL-gCFL quantum critical point hosts a sharply defined Fermi surface without long-lived electronic quasiparticles. Immediately across the transition, the two layers of gCFL are unstable to forming an insulating phase. We discuss the topological properties of the insulator and various observable signatures associated with the DMIT. Some key ingredients of this proposal include Dirac-Chern-Simons theory, color superconductivity, dimensional decoupling, etc.



    Applied von Neumann Algebra

    10:00 AM-11:00 AM
    July 21, 2020

    We are interested in mathematical results which are stated entirely without reference to von Neumann algebras but whose proofs use von Neumann algebras in an essential way. The first stunning example is the Kaplansky result that ab=1 iff ba=1 in a group algebra over a field of characteristic zero. Connes’ noncommutative integration theory yields other examples. We will concentrate on a new example in the theory of zero sets of Bergman spaces where we are able to calculate a certain density of orbits of Fuchsian groups.


  • CMSA EVENT: CMSA Quantum Matter/Quantum Field Theory Seminar: Domain Wall Decorations, Anomalies, and Fermionic SPT
    9:30 AM-11:00 AM
    July 22, 2020

    In the constructions of symmetry-protected topological (SPT) states, we usually decorate lower-dimensional states to higher codimensional domain walls of the system. In this talk, we will argue that domain wall decorations are basically equivalent to spectral sequences in algebraic topology. I will first illustrate this idea in bosonic systems, with explicit formulas for all differentials on all pages in the Lyndon-Hochschild-Serre spectral sequence. These results are useful in bosonic systems with Lieb-Schultz-Mattis (LSM) theorems, SPT-LSM theorems, and symmetry-enriched gauge theories. The second part of the talk will focus on fermionic SPT states. Using domain wall decorations, we will give a systematic construction and classification of fermionic SPT states in 3+1 or lower dimensions. We can obtain the full classifications for arbitrary finite unitary Abelian symmetries and interacting 10-fold way. All the classifications are consistent with known results from other approaches such as point/loop braiding statistics and spin cobordisms.


  • CMSA EVENT: CMSA Geometry and Physics Seminar: Parabolic de Rham bundles: motivic vs periodic
    9:30 PM-10:30 PM
    July 27, 2020

    Let $C$ be a complex smooth projective curve. We consider the set of parabolic de Rham bundles over $C$ (with rational weights in parabolic structure). Many examples arise from geometry: let $f: X\to U$ be a smooth projective morphism over some nonempty Zariski open subset $U\subset C$. Then the Deligne–Iyer–Simpson canonical parabolic extension of the Gauss–Manin systems associated to $f$ provides such examples. We call a parabolic de Rham bundle \emph{motivic}, if it appears as a direct summand of such an example of geometric origin. It is a deep question in the theory of linear ordinary differential equations and in Hodge theory, to get a characterization of motivic parabolic de Rham bundles. In this talk, I introduce another subcategory of parabolic de Rham bundles, the so-called \emph{periodic} parabolic de Rham bundles. It is based on the work of Lan–Sheng–Zuo on Higgs-de Rham flows, with aim towards linking the Simpson correspondence over the field of complex numbers and the Ogus–Vologodsky correspondence over the finite fields. We show that motivic parabolic de Rham bundles are periodic, and conjecture that they are all periodic parabolic de Rham bundles. The conjecture for rank one case follows from the solution of Grothendieck–Katz p-curvature conjecture, and for some versions of rigid cases should follow from Katz’s work on rigid local systems. The conjecture implies that in a spread-out of any complex elliptic curve, there will be infinitely many supersingular primes, a result of N. Elkies for rational elliptic curves. Among other implications of the conjecture, we would like to single out the conjectural arithmetic Simpson correspondence, which asserts that the grading functor is an equivalence of categories from the category of periodic parabolic de Rham bundles to the category of periodic parabolic Higgs bundles. This is a joint work in progress with R. Krishnamoorthy.


  • CMSA EVENT: CMSA Social Science Applications Forum: Measuring Intangible Capital with Market Prices
    10:00 PM-11:00 PM
    July 27, 2020

    Despite the importance of intangibles in today’s economy, current standards prohibit the capitalization of internally created knowledge and organizational capital, resulting in a downward bias of reported assets. As a result, researchers estimate this value by capitalizing prior flows of R&D and SG&A. In doing so, a set of capitalization parameters, i.e. the R&D depreciation rate and the fraction of SG&A that represents a long-lived asset, must be assumed. Parameters now in use are derived from models with strong assumptions or are ad hoc. We develop a capitalization model that motivates the use of market prices of intangibles to estimate these parameters. Two settings provide intangible asset values: (1) publicly traded equity prices and (2) acquisition prices. We use these parameters to estimate intangible capital stocks and subject them to an extensive set of diagnostic analyses that compare them with stocks estimated using existing parameters. Intangible stocks developed from exit price parameters outperform both stocks developed by publicly traded parameters and those stocks developed with existing estimates. (Joint work with Ryan Peters and Sean Wang.)

    For security reasons, you will have to show your full name to join the meeting.


    10:00 AM-11:00 AM
    July 28, 2020

    The Clifford group is the most important set of quantum circuits that allow for an efficient classical description. It therefore forms an integral part of many protocols in quantum information, and it turns out that their properties can often be described in terms of representation-theoretic data. Motivated by these connections, we start our analysis by establishing an analogue of Schur-Weyl duality. As is the case for SW-duality between U(d) and  Sthe resulting description of the tth tensor power of the n-qubit Clifford group is independent of the number n of qubits! This uniform theory implies that, maybe surprisingly, several tasks in quantum information theory can be performed with a system-size independent amount of resources. Examples include: Testing whether an unknown state is a stabilizer state, and constructing unitary designs with few non-Clifford gates.