Fractional and integer quantum hall effects in the zeroth landau level in graphene, Phys. Rev. B, vol.88, p.115407, 2013. ,
Critical comparison of classical field theory and microscopic wave functions for skyrmions in quantum hall ferromagnets, Physical Review B, vol.56, issue.11, p.6795, 1997. ,
The early proofs of the theorem of campbell, baker, hausdorff, and dynkin. Archive for history of exact sciences, pp.295-358, 2012. ,
Ground state of a spin-1/2 charged particle in a two-dimensional magnetic field, Phys. Rev. A, vol.19, pp.2461-2462, 1979. ,
Graphene integer quantum hall effect in the ferromagnetic and paramagnetic regimes, Physical Review B, vol.74, issue.7, p.75422, 2006. ,
Geometry of quantum evolution, Physical review letters, vol.65, issue.14, p.1697, 1990. ,
Hopf term and the effective lagrangian for the skyrmions in a two-dimensional electron gas at small g factor, Physical review letters, vol.78, issue.11, p.2188, 1997. ,
, Vladimir Igorevich Arnol'd. Mathematical methods of classical mechanics, vol.60, 2013.
Su (n) quantum hall skyrmions, Physical Review B, vol.59, issue.20, p.13147, 1999. ,
Interacting electrons and quantum magnetism, 2012. ,
Proof of completeness of lattice states in the k q representation, Physical Review B, vol.12, issue.4, p.1118, 1975. ,
On a hilbert space of analytic functions and an associated integral transform part i, Communications on pure and applied mathematics, vol.14, issue.3, pp.187-214, 1961. ,
On a hilbert space of analytie functions and an associated integral transform. part ii. a family of related function spaces application to distribution theory, Communications on pure and applied mathematics, vol.20, issue.1, pp.1-101, 1967. ,
On the completeness of the coherent states, Reports on Mathematical Physics, vol.2, issue.4, pp.221-228, 1971. ,
Optically pumped nmr evidence for finite-size skyrmions in gaas quantum wells near landau level filling ? = 1, Phys. Rev. Lett, vol.74, pp.5112-5115, 1995. ,
Directly detected nuclear magnetic resonance of optically pumped gaas quantum wells, Phys. Rev. Lett, vol.72, pp.1368-1371, 1994. ,
Giant low temperature heat capacity of gaas quantum wells near landau level filling ? = 1, Phys. Rev. Lett, vol.76, pp.4584-4587, 1996. ,
Quantal phase factors accompanying adiabatic changes, In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol.392, pp.45-57, 1984. ,
Elementary particles and su(4), Physics Letters, vol.11, issue.3, pp.255-257, 1964. ,
Thermodynamically stable magnetic vortex states in magnetic crystals, Journal of magnetism and magnetic materials, vol.138, issue.3, pp.255-269, 1994. ,
Thermodynamically stable "vortices" in magnetically ordered crystals. the mixed state of magnets, Zh. Eksp. Teor. Fiz, vol.95, p.182, 1989. ,
Stability of Classical Solutions, Sov. J. Nucl. Phys, vol.24, p.449, 1976. ,
Discrete coherent states on the von neumann lattice, Physical Review B, vol.18, issue.12, p.6744, 1978. ,
DOI : 10.1103/physrevb.18.6744
Amplitudes on von neumann lattices, Journal of Mathematical Physics, vol.22, issue.5, pp.1090-1099, 1981. ,
DOI : 10.1063/1.524992
Zur quantenmechanik. ii, Zeitschrift für Physik, vol.35, issue.8, pp.557-615, 1926. ,
DOI : 10.1007/bf01328531
Zur quantenmechanik, Zeitschrift für Physik, vol.34, issue.1, pp.858-888, 1925. ,
DOI : 10.1007/bf01328531
Bloch electrons in a uniform magnetic field, Phys. Rev, vol.133, pp.1038-1044, 1964. ,
Charged skyrmions: A condensate of spin excitons in a two-dimensional electron gas, Physical Review B, vol.53, issue.15, p.10148, 1996. ,
Infinite symmetry in the quantum hall effect, Nuclear Physics B, vol.396, issue.2-3, pp.465-490, 1993. ,
Efficient computation of the zassenhaus formula, Computer Physics Communications, vol.183, issue.11, pp.2386-2391, 2012. ,
Electromagnetic absorption and kerr effect in quantum hall ferromagnetic states of bilayer graphene, Physical Review B, vol.92, issue.12, p.125426, 2015. ,
Collective modes of cP 3 skyrmion crystals in quantum hall ferromagnets, Phys. Rev. B, vol.76, p.125320, 2007. ,
Biased bilayer graphene as a helical quantum hall ferromagnet, Phys. Rev. B, vol.84, p.235301, 2011. ,
Adams representation and localization in a magnetic field, Physical Review B, vol.28, issue.2, p.811, 1983. ,
Canted antiferromagnetic and spin-singlet quantum hall states in double-layer systems, Phys. Rev. B, vol.58, pp.4672-4693, 1998. ,
Topologically protected zero modes in twisted bilayer graphene, Phys. Rev. B, vol.84, p.45436, 2011. ,
Enhanced electron mobility and high order fractional quantum hall states in alas quantum wells, Applied Physics Letters, vol.80, issue.9, pp.1583-1585, 2002. ,
Modular invariance, universality and crossover in the quantum hall effect, Nuclear Physics B, vol.554, issue.3, pp.487-513, 1999. ,
Lowest landau level bosonization, Phys. Rev. B, vol.71, p.45339, 2005. ,
Bosonization approach for bilayer quantum hall systems at ? T = 1, Phys. Rev. Lett, vol.97, p.186401, 2006. ,
Quantum hall ferromagnetism in graphene: Su(4) bosonization approach, Phys. Rev. B, vol.76, p.195431, 2007. ,
Spin textures in quantum hall systems, Topological Aspects of Condensed Matter Physics: Lecture Notes of the Les Houches Summer School, vol.103, 2014. ,
Entanglement skyrmions in multicomponent quantum hall systems, Phys. Rev. B, vol.78, p.195327, 2008. ,
Noncommutative field theory, Rev. Mod. Phys, vol.73, pp.977-1029, 2001. ,
Calculation of the coefficients in the campbell-hausdorff formula, Doklady Akademii Nauk SSSR, vol.57, p.31, 1947. ,
Thermodynamic theory of weak ferromagnetism in antiferromagnetic substances. SOVIET, PHYSICS JETP-USSR, vol.5, issue.6, pp.1259-1272, 1957. ,
Theory of helicoidal structures in antiferromagnets. 1. nonmetals, Sov. Phys. JETP, vol.19, pp.960-971, 1964. ,
, Theory of helicoidal structures in antiferromagnets. 3. SOVIET PHYSICS JETP-USSR, vol.20, p.665, 1965.
Gravitation, gauge theories and differential geometry, Physics reports, vol.66, issue.6, pp.213-393, 1980. ,
Geometry of the transport equation in multicomponent wkb approximations, Comm. Math. Phys, vol.176, issue.3, pp.701-711, 1996. ,
Ground-state structure in ? = 2 bilayer quantum hall systems, Phys. Rev. B, vol.71, p.125318, 2005. ,
Quantum hall ferromagnets, Reports on Progress in Physics, vol.72, issue.8, p.86502, 2009. ,
Spin-pseudospin coherence and cp 3 skyrmions in bilayer quantum hall ferromagnets, Physical review letters, vol.82, issue.17, p.3512, 1999. ,
Interlayer exchange interactions, su (4) soft waves, and skyrmions in bilayer quantum hall ferromagnets, Physical Review B, vol.65, issue.7, p.75311, 2002. ,
Su (4) skyrmions and activation energy anomaly in bilayer quantum hall systems, Physical Review B, vol.70, issue.12, p.125304, 2004. ,
Topological solitons in the noncommutative plane and quantum hall skyrmions, Physical Review D, vol.72, issue.8, p.85002, 2005. ,
Noncommutative geometry, extended w ? algebra, and grassmannian solitons in multicomponent quantum hall systems, Physical Review B, vol.67, issue.12, p.125314, 2003. ,
Quantum Hall effects: Field theoretical approach and related topics, 2008. ,
Lectures on Riemann surfaces, vol.81, 2012. ,
Conformal field theory, Graduate texts in contemporary physics, 1997. ,
Collective-excitation gap in the fractional quantum hall effect, Physical review letters, vol.54, issue.6, p.581, 1985. ,
Magneto-roton theory of collective excitations in the fractional quantum hall effect, Physical Review B, vol.33, issue.4, p.2481, 1986. ,
Quantum theory of the electron liquid, 2005. ,
Electronic properties of graphene in a strong magnetic field, Rev. Mod. Phys, vol.83, pp.1193-1243, 2011. ,
Analysis of a SU(4) generalization of halperin's wave function as an approach towards a SU(4) fractional quantum hall effect in graphene sheets, Phys. Rev. B, vol.75, p.241405, 2007. ,
The formal power series, Duke Mathematical Journal, vol.23, issue.1, pp.13-21, 1956. ,
Noncommutative solitons, Journal of High Energy Physics, issue.05, p.20, 2000. ,
Controllable valley splitting in silicon quantum devices, Nat Phys, vol.3, issue.1, pp.41-45, 2007. ,
Principles of algebraic geometry, 2014. ,
DOI : 10.1002/9781118032527
URL : https://onlinelibrary.wiley.com/doi/pdf/10.1002/9781118032527.fmatter
On the principles of elementary quantum mechanics, Physica, vol.12, issue.7, pp.405-460, 1946. ,
DOI : 10.1007/978-94-017-6065-2_1
Phase structure of non-commutative scalar field theories, Nuclear Physics B, vol.605, issue.1, pp.395-424, 2001. ,
Geometrical description of the fractional quantum hall effect, Physical review letters, vol.107, issue.11, p.116801, 2011. ,
When is a"wavefunction"not a wavefunction?: a quantum-geometric reinterpretation of the laughlin state, APS Meeting Abstracts, 2013. ,
, Geometry of landau orbits in the absence of rotational symmetry, 2015.
, Lie groups, Lie algebras, and representations: an elementary introduction, vol.222, 2015.
Holomorphic methods in analysis and mathematical physics. first summer school in analysis and mathematical physics,(cuernavaca morelos, Contemp. Math, p.260, 1998. ,
Skyrmion lattice in a two-dimensional chiral magnet, Physical Review B, vol.82, issue.9, p.94429, 2010. ,
Algebraic topology. Tsinghua University press, 2002. ,
Über quantentheoretische umdeutung kinematischer und mechanischer beziehungen, Zeitschrift für Physik, vol.33, issue.1, pp.879-893, 1925. ,
Geometric formulation of quantum mechanics, 2015. ,
Electron correlations in narrow energy bands, vol.276, pp.238-257, 1365. ,
Quantum mechanics and quantum hall effect on reimann surfaces, Nuclear Physics B, vol.413, issue.3, pp.735-753, 1994. ,
Field theory in a strong magnetic field and the quantum hall effect: Integer hall effect, Physical Review B, vol.42, issue.16, p.10610, 1990. ,
, Field theory on the von neumann lattice and the quantized hall conductance of bloch electrons. Physica E: Low-dimensional Systems and Nanostructures, vol.4, pp.37-55, 1999.
Remarks on boson commutation rules, Communications in Mathematical Physics, vol.4, issue.2, pp.92-122, 1967. ,
Composite fermions, 2007. ,
Pseudospin anisotropy classification of quantum hall ferromagnets, Phys. Rev. B, vol.63, p.35305, 2000. ,
Excitations from a filled landau level in the two-dimensional electron gas, Phys. Rev. B, vol.30, pp.5655-5668, 1984. ,
Particle-vortex duality from 3d bosonization, Phys. Rev. X, vol.6, p.31043, 2016. ,
Néel-type skyrmion lattice with confined orientation in the polar magnetic semiconductor gav4s8, Nature Materials, 2015. ,
Spectroscopic evidence for the localization of skyrmions near ? = 1 as T ? 0, Phys. Rev. Lett, vol.86, pp.5353-5356, 2001. ,
Phase diagram for the ? = 0 quantum hall state in monolayer graphene, Phys. Rev. B, vol.85, p.155439, 2012. ,
Full expansion of the baker-campbell-hausdorff formula, 2017. ,
Anyons in an exactly solved model and beyond, Annals of Physics, vol.321, issue.1, pp.2-111, 2006. ,
Cooperative ring exchange theory of the fractional quantized hall effect, Physical review letters, vol.56, issue.8, p.873, 1986. ,
Global phase diagram in the quantum hall effect, Physical Review B, vol.46, issue.4, p.2223, 1992. ,
Edge structure of graphene monolayers in the ? = 0 quantum hall state, Phys. Rev. B, vol.92, p.165110, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01218597
Geometry of the time-dependent variational principle in quantum mechanics, vol.140, 1981. ,
Boson-vortex-skyrmion duality, spin-singlet fractional quantum hall effect, and spin-1/2 anyon superconductivity, Physical review letters, vol.64, issue.12, p.1313, 1990. ,
DOI : 10.1103/physrevlett.64.1313
Chemical potential and quantum hall ferromagnetism in bilayer graphene, Science, vol.345, issue.6192, pp.58-61, 2014. ,
DOI : 10.1126/science.1251003
URL : http://arxiv.org/pdf/1401.0659
Su(3) quantum hall ferromagnetism in snte, Phys. Rev. Lett, vol.116, p.26803, 2016. ,
DOI : 10.1103/physrevlett.116.026803
URL : https://link.aps.org/accepted/10.1103/PhysRevLett.116.026803
Su(4) skyrmions in the ? = ±1 quantum hall state of graphene, Phys. Rev. Lett, vol.117, p.56806, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-02065952
Spin-valley skyrmions in graphene at filling factor ? = ?1, Phys. Rev. B, vol.95, p.245428, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01582402
Density-controlled quantum hall ferromagnetic transition in a two-dimensional hole system, Scientific Reports, vol.7, issue.1, p.2468, 2017. ,
Motion of electrons and holes in perturbed periodic fields, Phys. Rev, vol.97, pp.869-883, 1955. ,
The Skyrme Model: Fundamentals Methods Applications, 2012. ,
Spin excitations of a two-dimensional electron gas in the limit of vanishing landé g factor, Phys. Rev. Lett, vol.77, pp.4604-4607, 1996. ,
Pseudospin anisotropy of trilayer semiconductor quantum hall ferromagnets, Phys. Rev. B, vol.94, p.85304, 2016. ,
DOI : 10.1103/physrevb.94.085304
URL : http://arxiv.org/pdf/1607.07909
A universal hamiltonian for motion and merging of dirac points in a two-dimensional crystal, The European Physical Journal B, vol.72, issue.4, p.509, 2009. ,
Spontaneous interlayer coherence in double-layer quantum hall systems: Charged vortices and kosterlitz-thouless phase transitions, Physical Review B, vol.51, issue.8, p.5138, 1995. ,
DOI : 10.1103/physrevb.51.5138
URL : http://arxiv.org/pdf/cond-mat/9407031
Polarization and intensity of raman scattering from plasmons and phonons in gallium arsenide, Phys. Rev. Lett, vol.19, pp.849-852, 1967. ,
DOI : 10.1103/physrevlett.19.849
Anisotropic superexchange interaction and weak ferromagnetism, Phys. Rev, vol.120, pp.91-98, 1960. ,
Quantum mechanics as a statistical theory, Mathematical Proceedings of the Cambridge Philosophical Society, vol.45, issue.1, pp.99-124, 1949. ,
Skyrmion lattice in a chiral magnet, Science, vol.323, issue.5916, pp.915-919, 2009. ,
Tata lectures on theta. I, Progress in Mathematics, vol.28, 1983. ,
Topological properties and dynamics of magnetic skyrmions, Nat Nano, vol.8, issue.12, pp.899-911, 2013. ,
, Geometry, topology and physics, 2003.
Quantum many-particle systems, 1988. ,
Dynamics of band electrons in electric and magnetic fields: rigorous justification of the effective hamiltonians, Rev. Mod. Phys, vol.63, pp.91-127, 1991. ,
Quantum hall ferromagnetism in graphene, Phys. Rev. Lett, vol.96, p.256602, 2006. ,
Field-induced kosterlitz-thouless transition in the n = 0 landau level of graphene, Phys. Rev. Lett, vol.103, p.216801, 2009. ,
Unconventional quantum hall effect and berry/'s phase of 2[pi] in bilayer graphene, Nat Phys, vol.2, issue.3, pp.177-180, 2006. ,
Unitary representations of w infinity algebras, International Journal of Modern Physics A, vol.7, issue.25, pp.6339-6355, 1992. ,
Temperature and density dependence of the electron landé g factor in semiconductors, Phys. Rev. B, vol.53, pp.7911-7916, 1996. ,
Multi-component spin textures in quantum hall ferromagnets, 2015. ,
Spin-isospin textured excitations in a double layer at filling factor ? = 2, Phys. Rev. Lett, vol.83, pp.2250-2253, 1999. ,
Semiquantal and Semiclassical Dynamics of Gaussian Wave Packets, 1994. ,
On the completeness of a system of coherent states, Theoretical and Mathematical Physics, vol.6, issue.2, pp.156-164, 1971. ,
Exact classical solution for the 't hooft monopole and the julia-zee dyon, Phys. Rev. Lett, vol.35, pp.760-762, 1975. ,
Riemannian structure on manifolds of quantum states, Communications in Mathematical Physics, vol.76, issue.3, pp.289-301, 1980. ,
Engineering the quantum states of light in a kerr-nonlinear resonator by two-photon driving, npj Quantum Information, vol.3, p.18, 2017. ,
Dissipation due to a "valley wave" channel in the quantum hall effect of a multivalley semiconductor, Phys. Rev. Lett, vol.57, pp.126-129, 1986. ,
Quantum hall ferromagnets: Induced topological term and electromagnetic interactions, Physical Review B, vol.60, issue.20, p.14154, 1999. ,
Hall viscosity, orbital spin, and geometry: paired superfluids and quantum hall systems, Physical Review B, vol.84, issue.8, p.85316, 2011. ,
Spin-peierls, valence-bond solid, and néel ground states of lowdimensional quantum antiferromagnets, Phys. Rev. B, vol.42, pp.4568-4589, 1990. ,
Nucleation, stability and currentinduced motion of isolated magnetic skyrmions in nanostructures, Nature nanotechnology, vol.8, issue.11, pp.839-844, 2013. ,
Evidence for skyrmions and single spin flips in the integer quantized hall effect, Phys. Rev. Lett, vol.75, pp.4290-4293, 1995. ,
Die gegenwärtige situation in der quantenmechanik, Naturwissenschaften, vol.23, issue.49, pp.823-828, 1935. ,
Achim Rosch, and Naoto Nagaosa. Inertia, diffusion, and dynamics of a driven skyrmion, Phys. Rev. B, vol.90, p.174434, 2014. ,
A duality web in 2+1 dimensions and condensed matter physics, Annals of Physics, vol.374, pp.395-433, 2016. ,
String theory and noncommutative geometry, Journal of High Energy Physics, issue.09, p.32, 1999. ,
DOI : 10.1088/1126-6708/1999/09/032
URL : http://iopscience.iop.org/article/10.1088/1126-6708/1999/09/032/pdf
Quantum criticality beyond the landau-ginzburg-wilson paradigm, Phys. Rev. B, vol.70, p.144407, 2004. ,
Competing orders, nonlinear sigma models, and topological terms in quantum magnets, Physical Review B, vol.74, issue.6, p.64405, 2006. ,
Deconfined quantum critical points, Science, vol.303, issue.5663, pp.1490-1494, 2004. ,
DOI : 10.1142/9789814280709_0014
URL : http://arxiv.org/pdf/cond-mat/0311326
Two-dimensional electrons occupying multiple valleys in alas. physica status solidi (b), vol.243, pp.3629-3642, 2006. ,
W infinity and string theory, International Journal of Modern Physics A, vol.7, issue.28, pp.6953-6993, 1992. ,
Handbook series on semiconductor parameters, vol.1, 1996. ,
A non-linear field theory, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol.260, pp.127-138, 1300. ,
A unified field theory of mesons and baryons, Nuclear Physics, vol.31, pp.556-569, 1962. ,
DOI : 10.1016/0029-5582(62)90775-7
Broken su(4) symmetry and the fractional quantum hall effect in graphene, Phys. Rev. Lett, vol.112, p.126804, 2014. ,
DOI : 10.1103/physrevlett.112.126804
URL : http://arxiv.org/pdf/1310.1642
Skyrmions and the crossover from the integer to fractional quantum hall effect at small zeeman energies, Physical Review B, vol.47, issue.24, p.16419, 1993. ,
Theory of interlayer tunneling in bilayer quantum hall ferromagnets, Phys. Rev. Lett, vol.86, pp.1829-1832, 2001. ,
Equivalence classes of minimum uncertainty packets, Physical Review D, vol.1, issue.12, p.3217, 1970. ,
DOI : 10.1103/physrevd.1.3217
Equivalence classes of minimum-uncertainty packets. ii, Physical Review D, vol.4, issue.6, p.1925, 1971. ,
DOI : 10.1103/physrevd.1.3217
Quantum field theory on noncommutative spaces, Physics Reports, vol.378, issue.4, pp.207-299, 2003. ,
DOI : 10.1016/s0370-1573(03)00059-0
URL : http://arxiv.org/pdf/hep-th/0109162
Quantum hall effect and landau-level crossing of dirac fermions in trilayer graphene, Nat Phys, vol.7, issue.8, pp.621-625, 2011. ,
Shift and spin vector: New topological quantum numbers for the hall fluids, Physical review letters, vol.69, issue.6, p.953, 1992. ,
Landau level bosonization of a twodimensional electron gas, Phys. Rev. B, vol.55, pp.7347-7350, 1997. ,
Quantum tunneling in a kerr medium with parametric pumping, Physical Review A, vol.48, issue.3, p.2494, 1993. ,
Current algebra, baryons, and quark confinement, Nuclear Physics B, vol.223, issue.2, pp.433-444, 1983. ,
So(5) symmetry in the quantum hall effect in graphene, Phys. Rev. B, vol.90, p.235432, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-01117748
Collective modes and skyrmion excitations in graphene s u (4) quantum hall ferromagnets, Physical Review B, vol.74, issue.7, p.75423, 2006. ,
Spin and valley quantum hall ferromagnetism in graphene, Nat Phys, vol.8, issue.7, pp.550-556, 2012. ,
Tunable symmetry breaking and helical edge transport in a graphene quantum spin hall state, Nature, vol.505, issue.7484, pp.528-528, 2014. ,
Near room-temperature formation of a skyrmion crystal in thin-films of the helimagnet fege, Nature materials, vol.10, issue.2, pp.106-109, 2011. ,
,
, Real-space observation of a two-dimensional skyrmion crystal, Nature, vol.465, issue.7300, pp.901-904, 2010.
Generating quantum mechanical superpositions of macroscopically distinguishable states via amplitude dispersion, Phys. Rev. Lett, vol.57, pp.13-16, 1986. ,
Quantum mechanics in phase space: an overview with selected papers, World Scientific, vol.34, 2005. ,
The skyrme model, Physics Reports, vol.142, issue.1, pp.1-102, 1986. ,
Magnetic translation group, Phys. Rev, vol.134, pp.1602-1606, 1964. ,
Discrete weyl-heisenberg transforms, Journal of Mathematical Physics, vol.37, issue.8, pp.3815-3823, 1996. ,
Low dimensional sigma models, 1989. ,
Group theory in a nutshell for physicists, 2016. ,
The chern-simons-landau-ginzburg theory of the fractional quantum hall effect, International Journal of Modern Physics B, vol.06, issue.01, pp.25-58, 1992. ,
Experimental observation of the quantum hall effect and berry's phase in graphene, Nature, vol.438, issue.7065, pp.201-204, 2005. ,