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

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

2000-02-04

arxiv.org/abs/cond-mat/0002063v2

Nucl.Phys. B604 (2001) 551-579

Physics

Condensed Matter

Strongly Correlated Electrons

16 pages, a reference added

Scientific paper

10.1016/S0550-3213(01)00120-1

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 $\lambda$. 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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