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The persistent current of correlated electrons in a continuous one-dimensional ring with a single scatterer is calculated by solving the many-body Schrodinger equation for several tens of electrons interacting via the electron-electron (e-e) interaction of finite range. The problem is solved by the configuration-interaction (CI) and diffusion Monte Carlo (DMC) methods. The CI and DMC results are in good agreement. In both cases, the persistent current I as a function of the ring length L exhibits the asymptotic dependence I ∝ L −1−α typical of the Luttinger liquid, where the power α depends only on the e-e interaction. The numerical values of α agree with the known formula of the renormalisation-group theory.Key words: one-dimensional transport, mesoscopic ring, persistent current, electron-electron interaction PACS: 73.23.-b, 73.61.Ey A one-dimensional (1D) interacting electron system cannot be viewed as a Fermi liquid of non-interacting quasi-particles. Away from the charge-density-wave instability, the interacting 1D system is a Luttinger liquid in which the elementary excitations are of collective Bosonic nature (see the review [1]). The Luttinger liquid properties affect the 1D electron transport. An interesting example of such effect is the persistent electron current in a mesoscopic 1D ring. Magnetic flux φ piercing the mesoscopic ring gives rise to the persistent current which can be expressed (at T = 0K) as [2]where E0 is the eigenenergy of the many-body groundstate. If the ring is clean and the single-particle dispersion law is parabolic, the electron-electron (e-e) interaction does not affect the persistent current owing to the Galilean invariance of the problem. However, ifEmail address: roman.krcmar@savba.sk (R. Krčmár).a single scatterer (an impurity or a weak link) is introduced into the ring, the non-interacting and interacting result are expected to differ fundamentally. For non-interacting spinless electrons in the 1D ring containing a single scatterer with transmission probability |t k F | 2 ≪ 1, the resulting persistent current depends on the magnetic flux and ring length (L) as [3]

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