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Duncan Haldane constructed a two-dimensional lattice model with quantized Hall conductivity without a net applied magnetic field. The Haldane model separates the topological mechanism of the quantum Hall effect from the usual formation of Landau levels in a uniform field. Changing model parameters closes and reopens an energy gap, separating phases with different Hall responses. This provides a compact theoretical example in which the global structure of occupied electronic states determines a measurable transport coefficient.^[ref]

A physicist researching condensed matter physics.^[ref]

By Duncan Haldane, credited as F. D. M. Haldane. Physical Review Letters 47, 1840–1843. Published 21 December 1981. Inspected abstract: long-wavelength density fluctuations give a universal low-energy description of one-dimensional Bose and Fermi fluids, with renormalized parameters. The publisher record links an erratum, Physical Review Letters 48, 569 (1982); no claim to full-text access is made.

A Luttinger liquid is a low-energy description of many gapless one-dimensional interacting quantum fluids. Its natural excitations are collective density waves, rather than independent fermion-like quasiparticles. Long-distance correlations typically decay with interaction-dependent powers at zero temperature. The Luttinger parameter and a mode velocity encode much of that long-wavelength behavior.

A narrow channel containing interacting particles motivates the picture: in one dimension, density disturbances cannot spread around one another through transverse space, and collective motion becomes especially important. The description applies to suitable bosonic as well as fermionic fluids. Duncan Haldane's harmonic-fluid treatment explicitly identifies this shared low-energy structure in terms of long-wavelength density fluctuations and renormalized parameters.^[ref] A gap, strong lattice locking or additional low-energy modes can require an extended description, so one-dimensional geometry alone is not enough to establish a single Luttinger liquid theory.