Geometry of Quantum Hall States: April 18, 2016 – June 17, 2016

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Geometry of Quantum Hall States

Organized by Sasha Abanov, Tankut Can, Anton Kapustin, and Paul Wiegmann

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April 18, 2016 – June 17, 2016

The quantum Hall effect (QHE) is a fascinating and important phenomenon. Since its experimental discovery in the early 80’s the QHE continues to fuel work in experimental physics, metrology, fundamental theoretical physics and mathematics.

At very low temperatures and strong magnetic fields, highly entangled collective electronic quantum states are formed on surfaces of ultra clean doped semiconductors. Despite varying microscopic details and imperfections of materials, these states possess universal properties demonstrating very precise (up to 9 significant digits) quantization of the Hall conductivity in units of fundamental constants. Other observable features are: an excitation gap determined by electron interactions, fractional charge and statistics of elementary excitations, and chiral massless boundary modes with universal dynamics.

From a theoretical standpoint, the QHE can be viewed as a topological quantum field theory (TQFT) with a TQFT-CFT correspondence manifested as a bulk-boundary correspondence in QH systems. In the last decade, there has been progress in understanding this connection with TQFT in the absence of relativistic invariance and in finding additional universal physical responses which are geometric in nature.

Many universal features of the QHE are also captured at the microscopic scale by model electron wave functions. An outstanding theoretical task is to connect this microscopic description with the macroscopic picture discussed above.

Recently, the physics of low energy transport phenomena has been connected to the response of the ground state to variations of the spatial geometry. This observation has led to a geometric description of QHE states, which links the physics of QH states to problems of modern geometry (Kahler geometry). Another rapidly developing link is a relation between the FQHE and the theory of random geometry and quantum gravity. The synthesis of subjects and intriguing links to modern mathematics give the QHE a very special status.

The goal of the program is to bring together physicists and mathematicians working on topics related to the geometry of QH states, in order to develop a geometric approach to quantum Hall states. The program will also encourage a broader discussion of the role of geometry in quantum states of condensed matter systems. Some of the key topics of the program are:

  • QH wave functions in geometric backgrounds
  • Effective field theory and geometric responses of QH states
  • Transport properties in inhomogeneous backgrounds
  • Bulk-boundary correspondence of QH states
  • Entanglement and topological order in QH states
  • Hydrodynamics of fractional QH electronic fluid
  • Methods of Conformal Field Theory and QH states
  • Other topics and connections to other systems (anomalous hydrodynamics, quantum gravity, random matrices, Kahler geometry)

Speaker and Seminar Schedule:

The weekly talks take place on Mondays, Wednesday and Fridays at 10:30am in room 313.

 

Date and Time Title Presenters
4/25 at 10:30am – Room 313  Galilean invariance at quantum Hall edge Sergej Moroz
4/27 at 10:30am – Room 313  Towards the classification of gapped phases of matter Ryan Thorngren
4/29 at 10:30am – Room 313 Non-commutative geometry techniques for aperiodic condensed matter systems Emil Prodan
5/2 at 10:30am – Room 313  Geometric deformation and Berry curvature in quantum Hall states Barry Bradlyn
5/4 at 10:30am – Room 313 The holographic Weyl semi-metal Karl Landsteiner
5/4 at 1:00pm – Room 313 Mathematical physics of map enumeration Peter Zograf
5/6 at 10:30am – Room 313 Electromagnetic response of semimetals from wavefunction geometry and topology Joel Moore
5/9 at 10:30am – Room 313 CANCELLED
5/10 at 10:30am – Room 313 Hall viscosity from Hall conductivity in Dirac crystals Maria A. H. Vozmediano
5/11 at 10:30am – Room 313 Anyons from braiding fluxes in the Pauli Hamiltonian Yosi Avron
5/13 at 10:30am – Room 313  CANCELLED
5/16 at 10:30am – Room 313  The Nematic Fractional Quantum Hall State and the interplay of Geometry and Topology Eduardo H Fradkin
5/18 at 10:30am – Room 313  Geometric Defects in FQH states Andrey Gromov
5/20 at 10:30am – Room 313  CANCELLED
5/23 at 10:30am – Room 313  Fractional Quantum Hall Effect on Singular Surfaces Misha Laskin
5/25 at 10:30am – Room 313  Hydrodynamics with non-Abelian currents: from spin Hall effect to quark-gluon plasma Piotr Surowka
5/26 at 2:00pm – Room 313  Particle Formation and Ordering in Strongly Correlated Fermionic Systems: Solving a Model of Quantum Chromodynamics Alexei Tsvelik
5/27 at 10:30am – Room 313  Absolute Stability without Topological Order Shivaji Sondhi
6/1 at 10:30am – Room 313  Jack Polynomials as Quantum Hall States Boris Hanin
6/3 at 10:30am – Room 313  Questions around Laughlin states on Riemann surfaces Semyon Klevtsov
6/6 at 10:30am – Room 313  CANCELLED
6/8 at 10:30am – Room 313  Questions around Laughlin states on Riemann surfaces, part 2 Semyon Klevtsov
6/10 at 10:30am – Room 313  Hydrodynamics with Hall viscosity: variational approach Alexander Abanov
6/13 at 10:30am – Room 313  CANCELLED
6/15 at 10:30am – Room 313   Newton-Cartan geometry and hydrodynamics with Hall viscosity Gustavo Monteiro
6/16 at 1:30pm – Room 313   Formalism for the solution of quadratic Hamiltonians with large cosine terms Sriram Ganeshan
6/17 at 10:30am – Room 313 Quasi-electrons on the sphere and jack polynomials Boris Hanin