A quest for Pfaffian Milica V. Milovanović Institute of Physics Belgrade Scientific Computing Laboratory (Talk at Physics Faculty, Belgrade, 2010)

Slides:

Advertisements

Similar presentations

Observation of a possible Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state in CeCoIn 5 Roman Movshovich Andrea Bianchi Los Alamos National Laboratory, MST-10.

Advertisements

Spintronics with topological insulator Takehito Yokoyama, Yukio Tanaka *, and Naoto Nagaosa Department of Applied Physics, University of Tokyo, Japan *

Capri Spring School Current Topics in Quantum Hall Research Allan MacDonald University of Texas at Austin.

Emergent Majorana Fermion in Cavity QED Lattice

Anyon and Topological Quantum Computation Beijing Normal university

High T c Superconductors & QED 3 theory of the cuprates Tami Pereg-Barnea

Quantum “disordering” magnetic order in insulators, metals, and superconductors HARVARD Talk online: sachdev.physics.harvard.edu Perimeter Institute, Waterloo,

Topological Superconductors

Detecting collective excitations of quantum spin liquids Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu.

Superconducting transport  Superconducting model Hamiltonians:  Nambu formalism  Current through a N/S junction  Supercurrent in an atomic contact.

Non-Abelian Anyon Interferometry Collaborators:Parsa Bonderson, Microsoft Station Q Alexei Kitaev, Caltech Joost Slingerland, DIAS Kirill Shtengel, UC.

Subir Sachdev arXiv: Subir Sachdev arXiv: Loss of Neel order in insulators and superconductors Ribhu Kaul Max Metlitski Cenke Xu.

Twist liquids and gauging anyonic symmetries

Fermi Gas Model Heisenberg Uncertainty Principle Particle in dx will have a minimum uncertainty in p x of dp x dx pxpx Next particle in dx will have.

Fractional topological insulators

B.Spivak University of Washington with S. Kivelson, S. Sondhi, S. Parameswaran A typology of quantum Hall liquids. Weakly coupled Pfaffian state as a type.

Fractional Quantum Hall states in optical lattices Anders Sorensen Ehud Altman Mikhail Lukin Eugene Demler Physics Department, Harvard University.

Two talks for the price of one: Cooling by angulon annihilation and Asymmetrical fermion superfluids P. Bedaque (Berkeley Lab) G. Rupak, M. Savage, H.

Majorana Fermions and Topological Insulators

Correlated tunneling and the instability of the fractional quantum Hall edge Dror Orgad Oded Agam July 21, 2009 PRL 100, (2008)

Theoretical Considerations and Experimental Probes of the =5/2 Fractional Quantized Hall State by Bertrand I. Halperin, Harvard University talk given at.

Robustness of Topological Superconductivity in Proximity-Coupled Topological Insulator Nanoribbons Tudor D. Stanescu West Virginia University Collaborators:

Probing and Manipulating Majorana Fermions in SO Coupled Atomic Fermi Gases Xia-Ji Liu CAOUS, Swinburne University Hawthorn, July.

Topological Insulators and Beyond

Quantum Antiferromagnetism and High T C Superconductivity A close connection between the t-J model and the projected BCS Hamiltonian Kwon Park.

6. Second Quantization and Quantum Field Theory

Kaiserslautern, April 2006 Quantum Hall effects - an introduction - AvH workshop, Vilnius, M. Fleischhauer.

Introduction to fractional quantum Hall effect Milica V. Milovanović Institute of Physics Belgrade Scientific Computing Laboratory (Talk at Physics Faculty,

Germán Sierra IFT-CSIC/UAM, Madrid in collaboration with Ignacio Cirac and Anne Nielsen MPQ,Garching Workshop: ”New quantum states of matter in and out.

Fermionic quantum criticality and the fractal nodal surface Jan Zaanen & Frank Krüger.

1 Topological Quantum Phenomena and Gauge Theories Kyoto University, YITP, Masatoshi SATO.

© Simon Trebst Interactions and disorder in topological quantum matter Simon Trebst University of Cologne Simon Trebst University of Cologne January 2012.

Oscillations of longitudina resistivity =Shubnikov-deHaas, minima close to 0. Plateaux in Hall resistivity  =h/(ne 2 ) with integer n correspond to the.

Correlated States in Optical Lattices Fei Zhou (PITP,UBC) Feb. 1, 2004 At Asian Center, UBC.

Introduction to even-denominator FQHE: composite fermions Tejas Deshpande Journal club: 11 November, 2014.

Topological Insulators and Topological Band Theory

Shell Model with residual interactions – mostly 2-particle systems Start with 2-particle system, that is a nucleus „doubly magic + 2“ Consider two identical.

Ady Stern (Weizmann) Papers: Stern & Halperin , PRL

The Helical Luttinger Liquid and the Edge of Quantum Spin Hall Systems

Condensed matter physics in dilute atomic gases S. K. Yip Academia Sinica.

Topological Quantum Computing

Electron-hole duality and vortex formation in quantum dots Matti Manninen Jyväskylä Matti Koskinen Jyväskylä Stephanie Reimann Lund Yongle Yu Lund Maria.

Fractional Statistics of Quantum Particles D. P. Arovas, UCSD Major ideas:J. M. Leinaas, J. Myrheim, R. Jackiw, F. Wilczek, M. V. Berry, Y-S. Wu, B. I.

Charge pumping in mesoscopic systems coupled to a superconducting lead

Disordering of a quantum Hall superfluid M.V. Milovanovic, Institute of Physics, Belgrade, Serbia.

The Puzzling Boundaries of Topological Quantum Matter Michael Levin Collaborators: Chien-Hung Lin (University of Chicago) Chenjie Wang (University of Chicago)

Basics of edge channels in IQHE doing physics with integer edge channels studies of transport in FQHE regime deviations from the ‘accepted’ picture Moty.

Subir Sachdev Superfluids and their vortices Talk online:

Entanglement and Topological order in self-dual cluster states Vlatko Vedral University of Oxford, UK & National University of Singapore.

Spectral function in Holographic superconductor Wen-Yu Wen (NTU) Taiwan String Theory Workshop 2010.

Dirac’s inspiration in the search for topological insulators

1 The 5/2 Edge IPAM meeting on Topological Quantum Computing February 26- March 2, 2007 MPA Fisher, with Paul Fendley and Chetan Nayak Motivation: FQHE:

Arnau Riera, Grup QIC, Dept. ECM, UB 16 de maig de 2009 Intoduction to topological order and topologial quantum computation.

From fractionalized topological insulators to fractionalized Majoranas

Fractional Berry phase effect and composite particle hole liquid in partial filled LL Yizhi You KITS, 2017.

Electrons-electrons interaction

Topological Insulators

Quantum Hall Fluids By Andrew York 12/5/2008.

QHE discovered by Von Klitzing in 1980

Majorana Fermions in Condensed-Matter Physics

Topological Order and its Quantum Phase Transition

D. Ferraro N. Magnoli M. Merlo

Non- Abelian Quantum Hall States:

Correlations of Electrons in Magnetic Fields

Majorana Spin Diagnostics

Quantum Computing: the Majorana Fermion Solution

SOC Fermi Gas in 1D Optical Lattice —Exotic pairing states and Topological properties 中科院物理研究所胡海平 Collaborators : Chen Cheng, Yucheng Wang, Hong-Gang.

Application of BCS-like Ideas to Superfluid 3-He

Sep. 23, 2008 Correlated tunneling and the instability of the fractional quantum Hall edge Dror Orgad Oded Agam PRL 100, (2008)

FSU Physics Department

Presentation transcript:

A quest for Pfaffian Milica V. Milovanović Institute of Physics Belgrade Scientific Computing Laboratory (Talk at Physics Faculty, Belgrade, 2010)

Hall experiment:

T= 85mKPlateaus ! Rigidity !filling factor = J.P.Eisenstein and H.L.Stormer, Science 248,1461(1990)

In rotationally symmetric gauge in two dimensions: Single particle wave functions: Orbits at radius: Imagine that we are at the middle of the plateau at 1/3 - How the ground state of the system would look like?

Laughlin answer: antisymmetry and in the cases of other “hierarchical constructions” odd denominator expected! R.B. Laughlin, PRL 50, 1995 (1983)

W. Pan et al.,PRL 83, 3530,1999. FQHE at 5/2 ! R. Willet et al., PRL 59, 1776, 1987

Theoretical Moore-Read answer : Pfaffian Pfaffian part describes a pairing among particles as in a superconductor = BCS pairing of spinless fermions G. Moore and N. Read, Nucl. Phys. B 360, 362 (1991)

Pfaffian for 4 particles: p-wave superconductor (p-ip) pairing functionwave function of a pair

Effective theory of a p-wave superconductor N. Read and D.Green, PRB 61,10267(2000) i.e. BCS mean field theory for eigenfunction of rotations in for eigenvalue

Excitations by Bogoliubov: a gapped system Ground state “weak pairing”

should not be too large: If large: (a)local maximum then likely: (b) local minimum i.e. Fermi liquid phase

FQHE systems (a) 5/2 : numerics favorable for Pfaffian in 2 nd LL Pfaffian is the most simple ansatz if not only explanation of plateau, R.H. Morf, PRL 80, 1505 (1998), E.H. Rezayi and F.D.M. Haldane, PRL 84, 4685 (2000) (b) 1/2 : exps. and numerics find Fermi-liquid-like phase (no plateau), E. Rezayi and N. Read, PRL 72, 900 (1994)

at 1/2 (1/4) in WQWs (wide quantum wells): signatures of FQHE – minima in ! likely nature of these states is multi-component (two-component) J. Shabani et al., Phys. Rev. Lett. 103, (2009)

theory (mathematical identity) two-component:

Pf state can lead to a first topological quantum computer! We want to know how to make Pfaffian!

BCS formalism of : with tunneling chemical potentials of parts: even: odd: grows with tunneling!

BCS formalism of : likely outcome: Fermi liquid If i.e. an open system then we may have a path: with Pfaffian outcome

How to recognize Pfaffian? Pfaffian makes a topological phase ! What are the signatures of a topological phase? (a) gap (b) characteristic degeneracy of ground state on higher genus surfaces like torus X.-G. Wen, Int. J. Mod. Phys. B 6, 1711 (1992)

Torus Create a qp-qh pair, separate and drag in opposite directions along one of the two distinct paths of torus and annihilate: a global process

Cylinder: To go to the other side requires energy (gapped excitations) and we may not end up with the same ground state but a new sector

FQH state:Filling factor:Degeneracy on torus: Laughlin 1/3 3 Moore-Read Pfafian 1/2 2 3 (331) 1/ – number connected with quasiparticles of Pfaffian: neutral fermions and vortices of the underlying superconductor, M. Milovanovic and N.Read, PRB53, (1996)

Numerics with tunneling, Z. Papic et al., arxiv: in a bilayer Sphere; overlap with tunneling: Sphere is biased for Pfaffian.

Torus; ground states with tunneling: No (clear) signatures of Pf degeneracy (2 – trivial degeneracy in a translatory invariant QH system at ½)

The quest for Pfaffian goes on!