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Characterization of One-Dimensional Luttinger Liquids in Terms of Fractional Exclusion Statistics

Yong-Shi Wu·Yue Yu·Huan-Xiong Yang
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Abstract

We develop a bosonization approach to study the low temperature properties of one-dimensional gas of particles obeying fractional exclusion statistics (FES). It is shown that such ideal gas reproduces the low-energy excitations and asymptotic exponents of a one-component Luttinger liquid (with no internal degrees of freedom). The bosonized effective theory at low energy (or temperature) is identified to a $c=1$ conformal field theory (CFT) with compactified radius determined by the statistics parameter $λ$. Moreover, this CFT can be put into a form of the harmonic fluid description for Luttinger liquids, with the Haldane controlling parameter identified with the statistics parameter (of quasi-particle excitations). Thus we propose to use the latter to characterize the fixed points of 1-d Luttinger liquids. Such a characterization is further shown to be valid for generalized ideal gas of particles with mutual statistics in momentum space and for non-ideal gas with Luttinger-type interactions: In either case, the low temperature behavior is controlled by an effective statistics varying in a fixed-point line.

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Yong-Shi Wu, Yue Yu, Huan-Xiong Yang. 2000-02-09. Characterization of One-Dimensional Luttinger Liquids in Terms of Fractional Exclusion Statistics. https://doi.org/10.1016/s0550-3213(01)00120-1

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