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arXiv:2411.14546 · Physical Review Research

Static impurity in a mesoscopic system of SU ( N ) fermionic matter waves

Juan Polo, Wayne Jordan Chetcuti, Anna Minguzzi, Andreas Osterloh, Luigi Amico A

Published Feb 23, 2026• 1 citation
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Abstract

We investigate the effects of a static impurity, modeled by a localized barrier, in a one-dimensional mesoscopic system comprised of strongly correlated repulsive SU ( N ) -symmetric fermions. For a mesoscopic sized ring under the effect of an artificial gauge field, we analyze the energy spectrum, the particle density, and the current flowing through the impurity at varying interaction strengths, barrier heights, and number of components. We find that the physics of the system is governed by the competition between effective single-particle process and the formation of a high-stiffness spin-correlated state associated with the phenomenon of fractionalization of the flux quantum characterizing the N -component fermionic system. Our findings provide a route to probe the response of SU ( N ) fermions to effective magnetic fields; at the same time, they hold significance for fundamental understanding of localized impurity problems.

DOI
10.1103/tcmp-nf52

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We investigate the effects of a static impurity, modeled by a localized barrier, in a one-dimensional mesoscopic system comprised of strongly correlated repulsive SU ( N ) -symmetric fermions. For a mesoscopic sized ring under the effect of an artificial gauge field, we analyze the energy spectrum, the particle density, and the current flowing through the impurity at varying interaction strengths, barrier heights, and number of components. We find that the physics of the system is governed by the competition between effective single-particle process and the formation of a high-stiffness spin-correlated state associated with the phenomenon of fractionalization of the flux quantum characterizing the N -component fermionic system. Our findings provide a route to probe the response of SU ( N ) fermions to effective magnetic fields; at the same time, they hold significance for fundamental understanding of localized impurity problems.
We consider a gas of repulsive N N -component fermions confined in a ring-shaped potential, subjected to an effective magnetic field. For large repulsion strengths, we work out a Bethe ansatz scheme to compute the two-point correlation matrix and then the one-particle density matrix. Our results hold in the mesoscopic regime of finite but sufficiently large number of particles and system size that are not accessible by numerics. We access the momentum distribution of the system and analyse its specific dependence of interaction, magnetic field and number of components N N . In the context of cold atoms, the exact computation of the correlation matrix to determine the interference patterns that are produced by releasing cold atoms from ring traps is carried out.
We study the persistent current in a system of SU(NNN) fermions with repulsive interaction confined in a ring-shaped potential and pierced by an effective magnetic flux. By applying a combination of Bethe ansatz and numerical analysis, we demonstrate that, as a combined effect of spin correlations, interactions and applied flux a specific phenomenon can occur in the system: spinon creation in the ground state. As a consequence, peculiar features in the persistent current arise. The elementary flux quantum, which fixes the persistent current periodicity, is observed to evolve from a single particle one to an extreme case of fractional flux quantum, in which one quantum is shared by all the particles. We show that the persistent current depends on the number of spin components NNN, number of particles and interaction in a specific way that in certain physical regimes has universality traits. At integer filling fractions, the persistent current is suppressed above a threshold of the repulsive interaction by the Mott spectral gap. Despite its mesoscopic nature, the current displays a clear finite size scaling behavior. Specific parity effects in the persistent current landscape hold.
The dynamics of a single impurity interacting with a many-particle background is one of the central problems of condensed-matter physics. Recent progress in ultracold-atom experiments makes it possible to control this dynamics by coupling an artificial gauge field specifically to the impurity. In this paper, we consider a narrow toroidal trap in which a Fermi gas is interacting with a single atom. We show that an external magnetic field coupled to the impurity is a versatile tool to probe the impurity dynamics. Using a Bethe ansatz, we calculate the eigenstates and corresponding energies exactly as a function of the flux through the trap. Adiabatic change of flux connects the ground state to excited states due to flux quantization. For repulsive interactions, the impurity disturbs the Fermi sea by dragging the fermions whose momentum matches the flux. This drag transfers momentum from the impurity to the background and increases the effective mass. The effective mass saturates to the total mass of the system for infinitely repulsive interactions. For attractive interactions, the drag again increases the effective mass which quickly saturates to twice the mass of a single particle as a dimer of the impurity and one fermion is formed. For excited states with momentum comparable to number of particles, effective mass shows a resonant behavior. We argue that standard tools in cold-atom experiments can be used to test these predictions.
We consider a one-dimensional mesoscopic Hubbard ring with and without disorder and compute charge and spin stiffness as a measure of the permanent currents. For finite disorder we identify critical disorder strength beyond which the charge currents in a system with repulsive interactions are larger than those for a free system. The spin currents in the disordered repulsive Hubbard model are enhanced only for small U, where the magnetic state of the system corresponds to a charge-density wave pinned to the impurities. For large U, the state of the system corresponds to localized isolated spins and the spin currents are found to be suppressed. For the attractive Hubbard model we find that the charge currents are always suppressed compared to the free system at all length scales.
We study the persistent current in a system of SU(N) fermions with repulsive interaction, confined in a ring-shaped potential and pierced by an effective magnetic flux. Several surprising effects emerge. As a combined result of spin correlations, (effective) magnetic flux and interaction, spinons can be created in the ground state such that the elementary flux quantum can change its nature. The persistent current landscape is affected dramatically by these changes. In particular, it displays a universal behaviour. Despite its mesoscopic character, the persistent current is able to detect a quantum phase transition (from metallic to Mott phases). Most of, if not all, our results could be experimentally probed within the state-of-the-art quantum technology, with neutral matter-wave circuits providing a particularly relevant platform for our work.
We study the persistent current and the Drude weight of a system of spinless fermions, with repulsive interactions and a hopping impurity, on a mesoscopic ring pierced by a magnetic flux, using a density matrix renormalization group (DMRG) algorithm for complex fields. Both the Luttinger liquid (LL) and the charge density wave (CDW) phases of the system are considered. Under a Jordan-Wigner transformation, the system is equivalent to a spin-1∕21∕21∕2 XXZXXZXXZ chain with a weakened exchange coupling. We find that the persistent current changes from an algebraic to an exponential decay with the system size, as the system crosses from the LL to the CDW phase with increasing interaction UUU. We also find that in the interacting system, the persistent current is invariant under the impurity transformation $\ensuremath{\rho}\ensuremath{\rightarrow}1∕\ensuremath{\rho}$, for large system sizes, where $\ensuremath{\rho}$ is the defect strength. The persistent current exhibits a decay that is in agreement with the behavior obtained for the Drude weight. We find that in the LL phase the Drude weight decreases algebraically with the number of lattice sites NNN, due to the interplay of the electron interaction with the impurity, while in the CDW phase, it decreases exponentially, defining a localization length which decreases with increasing interaction and impurity strength. Our results show that the impurity and the interactions always decrease the persistent current, and imply that the Drude weight vanishes in the limit $N\ensuremath{\rightarrow}\ensuremath{\infty}$ in both phases.