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The quantized Hall conductivity of integer and fractional quantum Hall (IQH and FQH) states is directly related to a topological invariant, the many-body Chern number.
Energy levels and wave functions of bloch electrons in rational and irrational magnetic fields
Douglas R. Hofstadter · 1976
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Quantized hall conductance in a two-dimensional periodic potential
D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs · 1982
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Quantized hall conductance as a topological invariant
Qian Niu, D. J. Thouless, and Yong-Shi Wu · 1985
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Topological invariant and the quantization of the hall conductance
Mahito Kohmoto · 1985
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Michael F Atiyah · 1988
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Marcel den Nijs and Koos Rommelse · 1989
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Edward Witten · 1989
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Ground-state degeneracy of the fractional quantum hall states in the presence of a random potential and on high-genus riemann surfaces
X. G. Wen and Q. Niu · 1990
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Topological Gauge Theories and Group Cohomology
Robbert Dijkgraaf and Edward Witten · 1990
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R. D. King-Smith and David Vanderbilt · 1993
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Quantum Field Theory of Many-Body Systems
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Characterization of topological insulators: Chern numbers for ground state multiplet
Yasuhiro Hatsugai · 2005
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Fractional quantum hall effect in optical lattices
Mohammad Hafezi, Anders Søndberg Sørensen, Eugene Demler, and Mikhail D Lukin · 2007
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Chetan Nayak, Steven H. Simon, Ady Stern, Michael Freedman, and Sankar Das Sarma · 2008
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Almost commuting matrices, localized wannier functions, and the quantum hall effect
Matthew B. Hastings and Terry A. Loring · 2010
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Exact parent hamiltonian for the quantum hall states in a lattice
Eliot Kapit and Erich Mueller · 2010
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Hannes Pichler, Guanyu Zhu, Alireza Seif, Peter Zoller, and Mohammad Hafezi · 2016
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Chiral ground-state currents of interacting photons in a synthetic magnetic field
Pedram Roushan, Charles Neill, Anthony Megrant, Yu Chen, Ryan Babbush, Rami Barends, Brooks Campbell, Zijun Chen, Ben Chiaro, Andrew Dunsworth, et al · 2017
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Quantum Origami: Transversal Gates for Quantum Computation and Measurement of Topological Order
Guanyu Zhu, Mohammad Hafezi, and Maissam Barkeshli · 2017
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Matrix product states and equivariant topological field theories for bosonic symmetry-protected topological phases in (1+1) dimensions
Ken Shiozaki and Shinsei Ryu · 2017
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Realizing and adiabatically preparing bosonic integer and fractional quantum hall states in optical lattices
Yin-Chen He, Fabian Grusdt, Adam Kaufman, Markus Greiner, and Ashvin Vishwanath · 2017
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On-chip quantum simulation with superconducting circuits
Andrew A Houck, Hakan E Türeci, and Jens Koch · 2012
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Frank Pollmann and Ari M. Turner · 2012
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Characterizing topological order by studying the ground states on an infinite cylinder
L. Cincio and G. Vidal · 2013
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Oscillating terms in the renyi entropy of fermi gases and liquids
Brian Swingle, Jeremy McMinis, and Norm M Tubman · 2013
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Exciton condensation in bilayer quantum hall systems
J.P. Eisenstein · 2014
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Many-body topological invariants for fermionic short-range entangled topological phases protected by antiunitary symmetries
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Topological exciton fermi surfaces in two-component fractional quantized hall insulators
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Many-body chern number without integration
Koji Kudo, Haruki Watanabe, Toshikaze Kariyado, and Yasuhiro Hatsugai · 2019
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Topological bands for ultracold atoms
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Topological photonics
Tomoki Ozawa, Hannah M. Price, Alberto Amo, Nathan Goldman, Mohammad Hafezi, Ling Lu, Mikael C. Rechtsman, David Schuster, Jonathan Simon, Oded Zilberberg, and Iacopo Carusotto · 2019
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Detecting fractional chern insulators through circular dichroism
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Symmetry fractionalization, defects, and gauging of topological phases
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Many-body topological invariants from randomized measurements
Andreas Elben, Jinlong Yu, Guanyu Zhu, Mohammad Hafezi, Frank Pollmann, Peter Zoller, and Benoît Vermersch · 2019
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Many-body physics with individually controlled rydberg atoms
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