Conformal properties of 1D quantum systems with long-range interactions

Details Conformal properties of 1D quantum systems with long-range interactions Conformal properties of 1D quantum systems with long-range interactions

2005-08-27

arxiv.org/abs/cond-mat/0508650v2

Phys.Rev.B72:245110,2005

Physics

Condensed Matter

Strongly Correlated Electrons

4 pages, no figures. Sectioning and references added. Content unchanged. To appear in Physical Review B

Scientific paper

10.1103/PhysRevB.72.245110

We investigate conformal properties of a one-dimensional quantum system with a long-range, Coulomb-like potential of the form $\frac{1}{|x|^{\sigma}}$, with $\sigma >0$. We compute the conformal anomaly $c$ as function of $\sigma$. We obtain $c=0$ for $\sigma <1$ (Wigner crystal) and $c=1$ for $\sigma >1$ (Luttinger liquid). By studying the scaling regime of the system when it is deformed by the inclusion of a term $t \rho(x)$, (with $\rho(x)$ a scaling operator), we show that, for $\sigma >1$, the correlation length $\xi$ gets an additional interaction dependent factor. This leads to a necessary redefinition of $\xi$ in order to avoid an unphysical dependence of the central charge on the coupling constant.

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