nLab Duncan Haldane

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Selected writings

A model for the fractional quantum Hall effect:

• F. Duncan M. Haldane: Fractional Quantization of the Hall Effect: A Hierarchy of Incompressible Quantum Fluid States, Phys. Rev. Lett. 51 (1983) 605 [doi:10.1103/PhysRevLett.51.605]

Observing what cane to be called the “Haldane gap phase of the antiferromagnetic integer Heisenberg spin chain model, the first example of a symmetry protected topological phase:

• F. Duncan M. Haldane: Nonlinear Field Theory of Large-Spin Heisenberg Antiferromagnets: Semiclassically Quantized Solitons of the One-Dimensional Easy-Axis Néel State, Phys. Rev. Lett. 50 (1983) 1153 [doi:10.1103/PhysRevLett.50.1153]

• Duncan Haldane, Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the $O(3)$ nonlinear sigma model, Physics Letters A 93 9 (1983) 464-468 [doi:10.1016/0375-9601(83)90631-X]

• Duncan Haldane: Ground State Properties of Antiferromagnetic Chains with Unrestricted Spin: Integer Spin Chains as Realisations of the $O(3)$ Non-Linear Sigma Model [arXiv:1612.00076]

Introducing the Haldane model and thereby predicting the quantum anomalous Hall effect:

• Duncan Haldane: Model for a Quantum Hall Effect without Landau Levels: Condensed-Matter Realization of the “Parity Anomaly”, Phys. Rev. Lett. 61 (1988) 2015 [doi:10.1103/PhysRevLett.61.2015]

Lecture:

• Duncan Haldane: Online course on topology in condensed matter, Haldane model, Berry curvature, and Chern number (2015-) [topocondmat.org/w4_haldane/haldane_model.html]

On parastatistics:

• F. Duncan M. Haldane: “Fractional statistics” in arbitrary dimensions: A generalization of the Pauli principle, Phys. Rev. Lett. 67 (1991) 937-940 [doi:10.1103/PhysRevLett.67.937, inSpire:321137]

On photonic crystals and topological photonics:

• Duncan Haldane, S. Raghu, Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry, Phys. Rev. Lett. 100 (2008) 013904 [doi:10.1103/PhysRevLett.100.013904]

Explicit computation of adiabatic braiding of pinned anyons in the Moore-Read state:

• Emil Prodan, F. Duncan Haldane: Mapping the braiding properties of the Moore-Read state, Phys. Rev. B 80 (2009) 115121 [doi:10.1103/PhysRevB.80.115121]

On excitations of fractional quantum Hall systems possibly identified as effective gravitons and gravitinos (cf. Supersymmetry in FQH systems):

• Bo Yang, Zi-Xiang Hu, Z. Papic, F. Duncan M. Haldane: Model Wavefunctions for the Collective Modes and the Magneto-roton Theory of the Fractional Quantum Hall Effect, Phys. Rev. Lett. 108 (2012) 256807 [doi:10.1103/PhysRevLett.108.256807, arXiv:1201.4165]

• Duncan Haldane: Majorana Physics, Neutral Fermion modes, and a “Gravitino”, in the Moore-Read Fractional Quantum Hall State, talk at Majorana Physics in Condensed Matter, Ettiore Majorana Center, Erice Italy (July 12-18, 2013) $[$pdf]

• Shiuan-Fan Liou, F. Duncan M. Haldane, Kun Yang, Edward H. Rezayi: Chiral Gravitons in Fractional Quantum Hall Liquids, Phys. Rev. Lett. 123 146801 (2019) [doi:PhysRevLett.123.146801, arXiv:1904.12231]

On the fractional quantum Hall effect:

• Duncan Haldane: Geometry of flux attachment in the fractional quantum hall effect states, lecture at CESC Cargèse Corsica July 2017, abstract published in: Topological Phase Transitions And New Developments, World Scientific (2018) 2 [pdf, pdf, doi:10.1142/9789813271340_0002]

On multiple modes replacing the would-be single GMP mode for FQH excitations near filling fraction $1/4$:

• Dung Xuan Nguyen, F. D. M. Haldane, Edward H. Rezayi, Dam Thanh Son, Kun Yang: Multiple Magnetorotons and Spectral Sum Rules in Fractional Quantum Hall Systems, Phys. Rev. Lett. 128 (2022) 246402 [doi:10.1103/PhysRevLett.128.246402, arXiv:2111.10593, suppl:pdf]

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