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F. Duncan M. Haldane

Duncan Haldane In general, I am interested in strongly-interacting quantum many-body condensed-matter systems, explored by non-perturbative methods:

Quantum Hall effect: I have been studying the stucture and stability of edges between different quantum Hall states of the two-dimensional electron gas. This is relevant to issues of edge transport, and also to observed transitions between different QHE states at the same Landau filling factor as quantum-well parameters are changed. I have also been studying the nature of the "Fermi surface" that appears in a half-filled Landau level, taking a microscopic viewpoint that should complement the effective Chern-Simons fermion approach of Halperin, Lee and Read.

Fractional Statistics: A few years ago, studies of integrable models (below) led me to formulate a description of fractional statistics based on a generalized Pauli exclusion principle, now called "exclusion statistics"; this is closely related to the "anyon" formulation. I have been interested in applications of this in one and two dimensions.

Integrable 1D Systems: We have been studying the remarkable correlation functions of the integrable one-dimensional systems with 1/r2 interactions (Calogero-Sutherland, and Haldane-Shastry models). These models may be thought of as describing an "ideal gas with fractional statistics". These are the first non-trivial models for which explicit correlation functions have been found exactly, and can be studied in detail.

Luttinger liquids and quantizing the Fermi surface: I have also been studying the extension of one-dimensional "bosonization" techniques to describe Fermi-surface degrees of freedom in higher dimensions. This provides a new viewpoint for Fermi-liquid theory, and suggests possibilities for possible breakdown of FLT in dimensions greater than one. I am attempting to incorporate gauge-field couplings to the Fermi surface degrees of freedom for describing the half-filled Landau level.

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S e l e c t e d P u b l i c a t i o n s:

  • F. D. M. Haldane
    Stability of Chiral Luttinger Liquids and Abelian Quantum Hall States
    Phys. Rev. Lett. 74, (1995).

  • F. D. M. Haldane
    Luttinger's Theorem and Bosonization of the Fermi Surface
    in Perspectives in Many-Particle Physics, eds. R. Broglia and J. R. Schrieffer, (North Holland, Amsterdam 1994, pp 5-30).

  • Z. N. C. Ha and F. D. M. Haldane
    Correlation Functions of the Supersymmetric t-J model with Inverse-Square Exchange
    Phys. Rev. Lett. 73, 2887 (1994).

  • F. D. M. Haldane and J. C. Talstra
    Dynamical T=0 Correlations of the S= 1/2 One-Dimensional Heisenberg Antiferromagnet with 1/r2 Exchange in a Magnetic field
    Phys. Rev. B 50, 6889 (1994).

  • F. D. M. Haldane
    Physics of the Ideal Semion Gas: Spinons and Quantum Symmetries of the Integrable Haldane-Shastry Spin Chain
    in Correlation Effects in Low-Dimensional Electron Systems, eds. A. Okiji and N. Kawakami, (Springer, Berlin, New York 1994, pp 3-20).

  • F. D. M. Haldane and M. R. Zirnbauer
    Exact calculation of the Ground-State Dynamical Spin Correlation Function of a S =1/2 Antiferromagnetic Heisenberg Chain with Free Spinons
    Phys. Rev. Lett. 71, 4055 (1993).

  • F. D. M. Haldane
    Fractional Statistics in Arbitrary Dimensions: A Generalization of the Pauli Principle
    Phys. Rev. Lett. 67, 937 (1991).


 
 

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