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arXiv:2011.00916 · SciPost Physics

Persistent current of SU(N) fermions

Wayne Jordan Chetcuti, Tobias Haug, L. C. Kwek, Luigi Amico A

Published Jan 21, 2022• 2 citations
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Abstract

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.

DOI
10.21468/scipostphys.12.1.033

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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 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.
Ultracold atomic systems have emerged as strong contenders amongst the various quantum systems relevant for developing and implementing quantum technologies due to their enhanced control and flexibility of the operating conditions. In this thesis, we explore persistent currents generated in a ring-shaped quantum gas of strongly interacting \textit{N}-component fermions, specifically the so-called SU(\textit{N}) fermions. Our results, apart from being a relevant contribution to many-body physics, prove the `primum mobile' for a new concept of matter-wave circuits based on SU(\textit{N}) fermionic platforms, opening an exciting chapter in the field of atomtronics. Indeed, the specific properties of quantization are expected to provide the core to fabricate quantum devices with enhanced sensitivity like interferometers. At the same time, SU(\textit{N}) fermionic circuits show promise in engineering cold atoms quantum simulators with this artificial fermionic matter.
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.
We study the persistent currents of an interacting Fermi gas confined in a tightly confining ring trapand subjected to an artificial gauge field. For attractive interactions, we study the currents all through the BCS-BEC crossover. At weak attractions, on theBCS side, fermions display a parity effect in the persistent currents, i.e. their response to the gauge fieldis paramagnetic or diamagnetic depending on the number of pairs on the ring. At resonance and on theBEC side of the crossover, we find a halving of the periodicity of the ground-state energy as a function ofthe artificial gauge field and disappearance of the parity effect, indicating that persistent currents can beused to infer the formation of tightly-bound bosonic pairs. We analyze then the readout of current states by spiral interferograms, showing that Fermi gases display an intrinsic reduction of coherence. Finally we show that the spin-resolved density-density correlator obtained from the expanding fermions at long times allows to probe the halving of the periodicity of the persistent currents and also yields information on quasi-off diagonal long range order.
Gauge theories arise in physical systems displaying space-time local symmetries. They provide a powerful description of important realms of physics ranging from fundamental interactions to statistical mechanics, condensed matter, and, more recently, quantum computation. As such, a remarkably deep understanding has been achieved in the field. With the advent of quantum technology, lower energy analogs, capable of capturing important features of the original quantum field theories through quantum simulation, have been intensively studied. Here, we propose a specific scheme implementing an quantum simulation of lattice gauge theories constrained to mesoscopic spatial scales. To this end, we study the dynamics of mesons residing in a ring-shaped lattice of mesoscopic size pierced by an effective magnetic field. In particular, we find a type of Aharonov-Bohm effect that goes beyond the particlelike effect, reflecting the features of the confining gauge potential. The coherence properties of the meson are quantified by the persistent current and by specific features of the correlation functions. When the magnetic field is quenched, Aharonov-Bohm oscillations and correlations start a specific matter-wave current dynamics. Published by the American Physical Society 2024