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Journal of the Physical Society of Japan

Persistent Current in Bose–Fermi Mixture on a Ring

Somei Suga, Tomonori Egawa, Akiko Masaki, 弘之 森

Published Jan 30, 2014• 2 citations
Publisher

Abstract

Persistent current of a Bose–Fermi mixture confined in a ring geometry threaded by a synthesized magnetic field is theoretically investigated. Numerical simulations are performed to study the role of boson–boson interactions and that of boson–fermion interactions on the transport property. The result shows that the boson–fermion interactions enhance the phase stiffness, which is a measure of the magnitude of the persistent current, more for the bosons than for the fermions. The same behavior is verified by a renormalization group calculation. The difference in the stiffness enhancement can be attributed to the difference in the localization property of the bosons and the fermions in one dimension.

DOI
10.7566/jpsj.83.024007

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Persistent current of a Bose–Fermi mixture confined in a ring geometry threaded by a synthesized magnetic field is theoretically investigated. Numerical simulations are performed to study the role of boson–boson interactions and that of boson–fermion interactions on the transport property. The result shows that the boson–fermion interactions enhance the phase stiffness, which is a measure of the magnitude of the persistent current, more for the bosons than for the fermions. The same behavior is verified by a renormalization group calculation. The difference in the stiffness enhancement can be attributed to the difference in the localization property of the bosons and the fermions in one dimension.
Bose–Fermi atom mixture systems confined in a ring geometry threaded by a synthesized magnetic field were theoretically investigated in numerical and analytical approaches. Numerical simulations were performed to study effects of the boson–boson interactions and boson–fermion interactions on phase stiffness. In the simulations, the phase stiffness was measured for repulsive and attractive boson–fermion interactions and found to increase with the repulsive interactions and decrease with the attractive ones. There was also a characteristic behavior found in the phase stiffness with the attractive interactions under a certain condition of the particle number. We confirmed these effects by renormalization group calculations including higher-order fluctuations.
The persistent current is here studied in one-dimensional disordered rings that contain interacting electrons. We used the density matrix renormalization group algorithms in order to compute the stiffness, a measure that gives the magnitude of the persistent currents as a function of the boundary conditions for different sets of both interaction and disorder characteristics. In contrast to its noninteracting value, an increase in the stiffness parameter was observed for systems at and off half-filling for weak interactions and nonzero disorders. Within the strong interaction limit, the decrease in stiffness depends on the filling and an analytical approach is developed to recover the observed behaviors. This is required in order to understand its mechanisms. Finally, the study of the localization length confirms the enhancement of the persistent current for moderate interactions when disorders are present at half-filling. Our results reveal two different regimes, one for weak and one for strong interactions at and off half-filling.
The persistent current in a lattice model of a one-dimensional interacting electron system is systematically studied using a complex version of the density-matrix renormalization group algorithm and the functional renormalization group method. We mainly focus on the situation where a single impurity is included in the ring penetrated by a magnetic flux. Due to the interplay of the electron-electron interaction and the impurity the persistent current in a system of N lattice sites vanishes faster than 1/N.1/N.1/N. Only for very large systems and large impurities our results are consistent with the Bosonization prediction obtained for an effective field theory. The results from the density-matrix renormalization group and the functional renormalization group agree well for interactions as large as half the bandwidth, even though as an approximation in the latter method the flow of the two-particle vertex is neglected. This confirms that the functional renormalization group method is a very powerful tool to investigate correlated electron systems. The method will become very useful for the theoretical description of the electronic properties of small conducting ring molecules.
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. We finally show that the spin-resolved density-density correlator obtained from the expansion of the 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.
We consider a two-component Bose–Bose mixture at infinitely strong repulsive interactions in a tightly confining, one-dimensional ring trap and subjected to an artificial gauge field. By employing the Bethe Ansatz exact solution for the many-body wavefunction, we obtain the ground state energy and the persistent currents up to four particles. For each value of the applied flux, we then determine the symmetry of the state under particles exchange. We find that the ground-state energy and the persistent currents display a reduced periodicity with respect to the case of non-interacting particles, corresponding to reaching states with fractional angular momentum per particle. We relate this effect to the change of symmetry of the ground state under the effect of the artificial gauge field. Our results generalize the ones previously reported for fermionic mixtures with both attractive and repulsive interactions and highlight the role of symmetry in this effect.
The persistent current and charge stiffness of a one-dimensional Luttinger liquid on a ring threaded by a magnetic flux are calculated by Monte Carlo simulation. By changing the random impurity potential strength and the electron-electron interaction, we see a crossover behavior between weak- and strong-impurity limits. For weak-impurity potentials, interactions enhance impurity effects, that is, interactions decrease the current and the stiffness. On the other hand, interactions tend to screen impurities when the impurity potential is strong. Temperature dependence of the persistent current and the charge stiffness shows a peak at a characteristic temperature, consistent with a recent single-impurity study.