Parity-locking effect in a strongly-correlated ring

Orbital magnetism in an integrable model of a multichannel ring with long-ranged electron-electron interactions is investigated. In a noninteracting multichannel system, the response to an external magnetic flux is the sum of many diamagnetic and paramagnetic contributions, but we find that for sufficiently strong correlations, the contributions of all channels add constructively, leading to a parity (diamagnetic or paramagnetic) which depends only on the total number of electrons. Numerical results confirm that this parity-locking effect is robust with respect to subband mixing due to disorder. The free energy F (φ) of a metallic ring threaded by an Aharonov-Bohm flux (h̄c/e)φ is a periodic function of φ, with period 2π [1]. The system is said to be diamagnetic if F is minimal for φ = 0, and paramagnetic if F is minimal for φ = π (1/2 flux quantum). A purely one-dimensional (1D) ring with N spinless electrons is diamagnetic if N is even and paramagnetic if N is odd, independent of disorder and interactions [2, 3]. This connection between the parity of N and the sign of the magnetic response of the system is sometimes referred to as Leggett’s theorem [2]. The persistent current I = −(e/h̄)∂F/∂φ is a periodic function of φ with amplitude I0 = evF /L in a clean 1D ring [4], where vF is the Fermi velocity and L the circumference of the ring. In a ring with many independent channels, I is the sum of many such diamagnetic and paramagnetic contributions, and thus has a random sign and small amplitude [1]. Leggett’s theorem is thus generally violated in multichannel systems. In an interacting system, the parities of different channels are no longer independent. In this article, we investigate the orbital magnetism of 1D SU(M) fermions interacting via the potential V (x) = g/x. We find that for g > 0, Leggett’s theorem is restored for an arbitrary number of channels M . In addition, provided the ring is sufficiently thin (kFL > 2πM) we find that the