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In these notes I survey geometric aspects of the lowest Landau level wave functions, integer quantum Hall state and Laughlin states on compact Riemann surfaces.
S. Lang, Introduction to Modular Forms
1976
Earlier work this paper cites.
P. Griffiths and J. Harris, Principles of Algebraic Geometry , John Wiley and Sons, New York, 1978
1978
Earlier work this paper cites.
B. A. Dubrovin and S. P. Novikov, Ground state of a two dimensional electron in a periodic magnetic field,
1980
Earlier work this paper cites.
R. B. Laughlin, Quantized Hall conductivity in two dimensions
1981
Earlier work this paper cites.
A. M. Polyakov, Quantum geometry of bosonic strings,
1981
Earlier work this paper cites.
D. J. Thouless, M. Kohmoto, M. P. Nightingale and M. den Nijs, Quantized Hall conductance in a two-dimensional periodic potential,
1982
Earlier work this paper cites.
J. E. Avron, R. Seiler and B. Simon, Homotopy and quantization in condensed matter physics,
1983
Earlier work this paper cites.
F. D. M. Haldane, Fractional quantization of the Hall effect: a hierarchy of incompressible quantum fluid states
1983
Earlier work this paper cites.
R. B. Laughlin, Anomalous quantum Hall effect: an incompressible quantum fluid with fractionally charged excitations
1983
Earlier work this paper cites.
D. Mumford, Tata lectures on theta I,
1983
Earlier work this paper cites.
B. Simon, Holonomy, the Quantum Adiabatic Theorem, and Berry’s Phase,
1983
Earlier work this paper cites.
M. V. Berry, Quantal phase factors accompanying adiabatic changes,
1984
Earlier work this paper cites.
B. I. Halperin, Statistics of quasiparticles and the hierarchy of fractional quantized Hall states,
1984
Earlier work this paper cites.
R. Tao and Y.-S. Wu, Gauge invariance and fractional quantum Hall effect,
1984
Earlier work this paper cites.
J. E. Avron and R. Seiler, Quantization of the Hall conductance for general, multiparticle Schrödinger hamiltonians,
1985
Earlier work this paper cites.
F. D. M. Haldane and E. H. Rezayi, Periodic Laughlin-Jastrow wave functions for the fractional quantized Hall effect
1985
Earlier work this paper cites.
Q. Niu, D. J. Thouless and Y.-S. Wu, Quantized Hall conductance as a topological invariant,
1985
Earlier work this paper cites.
D. Quillen, Determinants of Cauchy-Riemann operators over a Riemann surface,
1985
Earlier work this paper cites.
L. Alvarez-Gaume, G. Moore and C. Vafa, Theta functions, modular invariance, and strings,
1986
Earlier work this paper cites.
A. Belavin and V. Knizhnik, Algebraic geometry and the geometry of quantum strings,
1986
Earlier work this paper cites.
E. D’Hoker and D. H. Phong, On determinants of laplacians on riemann surfaces,
1986
Earlier work this paper cites.
L. Alvarez-Gaume, J.-B. Bost, G. Moore, P. Nelson and C. Vafa, Bosonization on higher genus Riemann surfaces,
1987
Earlier work this paper cites.
J.-M. Bismut and D. Freed, The analysis of elliptic families. I-II,
1987
Earlier work this paper cites.
P. Di Francesco, H. Saleur, J. B. Zuber, Relations between the Coulomb gas picture and conformal invariance of two-dimensional critical models,
1987
Earlier work this paper cites.
A. M. Polyakov, Quantum gravity in two dimensions,
1987
Earlier work this paper cites.
E. P. Verlinde and H. L. Verlinde, Chiral bosonization, determinants and the string partition function,
1987
Earlier work this paper cites.
P. G. Zograf and L. A. Takhtadzhyan, A local index theorem for families of ∂ ¯ \bar{\partial} -operators on Riemann surfaces,
1987
Earlier work this paper cites.
J.-M. Bismut, H. Gillet and C. Soulé, Analytic torsion and holomorphic determinant bundles. III,
1988
Earlier work this paper cites.
E. D’Hoker and D. H. Phong, The geometry of string perturbation theory,
1988
Earlier work this paper cites.
B. Osgood, R. Phillips and P. Sarnak, Extremals of determinants of laplacians,
1988
Earlier work this paper cites.
J. K. Jain, Composite-fermion approach for the fractional quantum Hall effect,
1989
Earlier work this paper cites.
R. Laughlin, Spin hamiltonian for which quantum Hall wave function is exact,
1989
Earlier work this paper cites.
X. G. Wen and Q. Niu, Ground-state degeneracy of the fractional quantum Hall states in the presence of a random potential and on high-genus Riemann surfaces
1990
Earlier work this paper cites.
J. Fröhlich and T. Kerler, Universality in quantum Hall systems,
1991
Earlier work this paper cites.
G. Moore and N. Read, Nonabelions in the fractional quantum Hall effect
1991
Earlier work this paper cites.
J. E. Avron, M. Klein, A. Pnueli and L. Sadun, Adiabatic Charge Transport and Persistent Currents of Leaky Tori,
1992
Cited alongside, same era.
A. H. Chamseddine and J. Fröhlich, Two dimensional Lorentz-Weyl anomaly and gravitational Chern-Simons theory,
1992
Cited alongside, same era.
J. Fay, Kernel functions, analytic torsion and moduli spaces,
1992
Cited alongside, same era.
J. Fröhlich and U. M. Studer, U ( 1 ) × S U ( 2 ) U(1)\times SU(2) -gauge invariance of non-relativistic quantum mechanics, and generalized Hall effects,
1992
Cited alongside, same era.
X. G. Wen and A. Zee, Shift and spin vector: New topological quantum numbers for the Hall fluids,
1992
Cited alongside, same era.
2007
Later among the works it cites.
2008
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D. H. Phong and J. Sturm, Lectures on stability and constant scalar curvature,
2009
Later among the works it cites.
2009
Later among the works it cites.
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1993
Cited alongside, same era.
E. Keski-Vakkuri and X. G. Wen, The ground state structure and modular transformations of fractional quantum Hall states on a torus,
1993
Cited alongside, same era.
J. E. Avron, R. Seiler and P. G. Zograf, Adiabatic quantum transport: quantization and fluctuations,
1994
Cited alongside, same era.
J. Bellissard, A. van Elst and H. Schulz-Baldes, The noncommutative geometry of the quantum Hall effect,
1994
Cited alongside, same era.
R. Iengo and D. Li, Quantum mechanics and quantum Hall effect on Riemann surfaces,
1994
Cited alongside, same era.
J. E. Avron, R. Seiler and P. G. Zograf, Viscosity of quantum Hall fluids,
1995
Cited alongside, same era.
J. Avron, Adiabatic quantum transport
1995
Cited alongside, same era.
2009
Later among the works it cites.
I. Tokatly and G. Vignale, Lorentz shear modulus of fractional quantum Hall states,
2009
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M. R. Douglas and S. Klevtsov, Bergman kernel from path integral,
2010
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2011
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F. D. M. Haldane, Geometrical description of the fractional quantum Hall effect,
2011
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2012
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H. Xu, A closed formula for the asymptotic expansion of the Bergman kernel,
2012
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M. Barkeshli, C.-M. Jian, and X.-L. Qi, Twist defects and projective non-Abelian braiding statistics,
2013
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T. Kvorning, Quantum Hall hierarchy in a spherical geometry,
2013
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H. Xu and S.-T. Yau, Trees and tensors on Kahler manifolds,
2013
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2013
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2014
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2014
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2014
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F. Ferrari and S. Klevtsov, FQHE on curved backgrounds, free fields and large N,
2014
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M. Fremling, T. H. Hansson and J. Suorsa, Hall viscosity of hierarchical quantum Hall states,
2014
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A. Gromov and A. G. Abanov, Density-curvature response and gravitational anomaly,
2014
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C. Hoyos, Hall viscosity, topological states and effective theories,
2014
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S. Klevtsov, Random normal matrices, Bergman kernel and projective embeddings,
2014
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2015
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2015
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2015
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A. Gromov and A. G. Abanov, Thermal Hall effect and geometry with torsion,
2015
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2015
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S. Klevtsov and P. Wiegmann, Geometric adiabatic transport in Quantum Hall states,
2015
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M. Laskin, T. Can and P. Wiegmann, Collective field theory for quantum Hall states
2015
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A. Cappelli, E. Randellini, Multipole expansion in the quantum hall effect,
2016
Closest in time.
A. Deshpande and A. Nielsen, Lattice Laughlin states on the torus from conformal field theory,
2016
Closest in time.
N. Schine, A. Ryou, A. Gromov, A. Sommer and J. Simon, Synthetic Landau levels for photons,
2016
Closest in time.
V. Kalmeyer and R. B. Laughlin, Equivalence of the resonating-valence-bond and fractional quantum Hall states,
2095
Closest in time.