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

Abstract

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.

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

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• Wigner Crystal in One Dimension
• Spin Waves in Antiferromagnetic Spin Chains with Long Range Interactions
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Cited by in corpus (1)

• Ground states of long-range interacting fermions in one spatial dimension