Hubbard Rings Research Articles

Current in Hubbard rings manipulated via magnetic flux

We study currents in a quantum ring threaded by a magnetic fluxwhich is varied in an arbitrary way from an initial constant valueϕ1 at timet1 to a final constantvalue ϕ2 at timet2. We analyze how theinduced currents for t > t2 can be controlled by the rate of flux variation . The dynamics of electrons in the ring is described using the Hubbard and the extendedHubbard models. In the Hubbard model with infinite on-site repulsion the current fort > t2 is shown to be independent of the flux variation beforet2 and is fully determined by a solution of the initial equilibrium problem and by the valueϕ2 of the flux. For intermediate values of the interaction strength the current displays regularor irregular time oscillations and the amplitude of oscillations is sensitive to the rate of theflux changing : slow changes of the flux result in small amplitudes of the current oscillations and viceversa. We demonstrate that the time dependence of the induced current bears informationon electronic correlations. Our results have important implications for not only mesoscopicrings but also the designing of quantum motors built out of ring-shaped optical lattices.

Analysis of the [formula omitted] Hubbard ring using counting operators

We prove three theorems about the use of a counting operator to study the spectrum of model Hamiltonians. We analytically calculate the eigenvalues of the Hubbard ring with four lattice positions and apply our theorems to describe the observed level crossings.

Persistent currents in the one-dimensional mesoscopic Hubbard ring

In this paper, we study persistent charge and spin currents in the ground state of theone-dimensional mesoscopic Hubbard ring with repulsive interaction based on itsBethe-ansatz solution. We find that the persistent charge current is suppressed bythe on-site Coulomb interaction more significantly at half-filling than away fromhalf-filling. As the system size increases the charge current decays exponentially asI∼L−1e−L/ξ in the half-filling case and decays in a power law away from the half-filling case. We alsofind that the persistent spin current is suppressed by the on-site Coulomb interaction, andit decays algebraically as the system size increases both at half-filling and away fromhalf-filling.

Persistent currents and spin-charge separation in a one-dimensional Hubbard ring with side sites

The persistent current and spin-charge separation are studied in a one-dimensional (1D) Hubbard ring with side sites connected to the even sites of the ring. At half filling, the persistent current is always paramagnetic and has a period of flux quantum. Away from half filling, as the onsite repulsion $U$ increases, the sign of the current may oscillate depending on the total number of electrons ${N}_{e}$ and the hopping $t$ between the ring site and the side site. For small hopping $t$, the number of electrons ${N}_{e}^{\ensuremath{'}}$ in the ring sites plays an important role in determining the sign of the current. In contrast to the 1D Hubbard model, a weak or a moderate $U$ can strongly enhance the persistent current while the hopping $t$ always suppresses the current. The study on the transmittance of the ring with two connected leads indicates that in the large $U$ and small $t$ case, the transmittance varies with a period $1∕{N}_{e}^{\ensuremath{'}}$ of a flux quantum, demonstrating a spin-charge separation in this system.

Cooper-pair transport through a Hubbard chain sandwiched between two superconductors: Density matrix renormalization group calculations

We present a numerical approach to study the coherent transport of Cooper pairs through a Hubbard chain, and study the role of the contacts in achieving perfect Andreev reflection. We calculate the pair transport using the Density Matrix Renormalization Group by measuring the response of the system to quantum pair fields with complex phases on the two ends of an open system. This approach gives an effective superfluid weight which is in close agreement with the Bethe Ansatz results for the superfluid weight for closed Hubbard rings.

Strange behavior of persistent currents in small Hubbard rings

We show exactly that small Hubbard rings exhibit unusual kink-like structures giving anomalous oscillations in persistent current. Singular behavior of persistent current disappears in some cases. In half-filled systems mobility gradually drops to zero with interaction, while it converges to some finite value in non-half-filled cases.

Detection of topological transitions by transport through molecules and nanodevices.

We analyze the phase transitions of an interacting electronic system weakly coupled to free-electron leads by considering its zero-bias conductance. This is expressed in terms of two effective impurity models for the cases with and without spin degeneracy. Using the half-filled ionic Hubbard ring, we demonstrate that the weight of the first conductance peak as a function of external flux or of the difference in gate voltages between even and odd sites allows one to identify the topological charge transition between a correlated insulator and a band insulator.

Half-filled Hubbard ring with alternating site potentials in a magnetic field

We have studied a Hubbard ring with alternating site potentials for half-filling in presence of a magnetic flux. Using a mean-field approach we have calculated the conductivity of such a ring at low and high temperatures. The interplay of the correlation, the polarizing field and the chemical modulation in site potentials tune the conductivity in an interesting fashion. In presence of the modulation in the site energy an appreciable variation in the conductance is observed with the change in flux. This scenario gets substantially modified in presence of the Hubbard correlation. Finite-size effects are also identified and they are found to be quickly disappearing with increasing system size. Sharp changes in the magnetoconductance is found to disappear at higher temperatures.

Persistent currents in small, imperfect Hubbard rings

We have done a study with small, imperfect Hubbard rings with exact diagonalization. The results for few-electron rings show, that the imperfection, whether localized or not, nearly always decrease, but can also \emph{increase} the persistent current, depending on the character of the imperfection and the on-site interaction. The calculations are generally in agreement with more specialized studies. In most cases the electron spin plays an important role.

Spin fluctuations in the quarter-filled Hubbard ring: Significances toLiV2O4

Using the quantum Monte Carlo method, we investigate the spin dynamics of itinerant electrons in the one-dimensional Hubbard system. Based on the model calculation, we have studied the spin-fluctuations in the quarter-filled metallic Hubbard ring, which is aimed at the vanadium ring or chain defined along corner-sharing tetrahedra of LiV$_2$O$_4$, and found the dramatic changes of magnetic responses and spin-fluctuation characteristics with the temperature. Such results can explain the central findings in the recent neutron scattering experiment for LiV$_2$O$_4$.

Spectral functions of half-filled one-dimensional Hubbard rings with varying boundary conditions

We study the effect of varying the boundary condition on the spectral function of a finite one-dimensional Hubbard chain, which we compute using direct (Lanczos) diagonalization of the Hamiltonian. By direct comparison with the two-body response functions and with the exact solution of the Bethe ansatz equations, we can identify both spinon and holon features in the spectra. At half-filling the spectra have the well-known structure of a low-energy holon band and its shadow---which spans the whole Brillouin zone---and a spinon band present for momenta less than the Fermi momentum. Features related to the twisted boundary condition are cusps in the spinon band. We show that the spectral building principle, adapted to account for both the finite system size and the twisted boundary condition, describes the spectra well in terms of single spinon and holon excitations. We argue that these finite-size effects are a signature of spin-charge separation and that their study should help establish the existence and nature of spin-charge separation in finite-size systems.

Finite-temperature transport in finite-size Hubbard rings in the strong-coupling limit

We study the current, the curvature of levels, and the finite temperature charge stiffness, D(T,L), in the strongly correlated limit, U>>t, for Hubbard rings of L sites, with U the on-site Coulomb repulsion and t the hopping integral. Our study is done for finite-size systems and any band filling. Up to order t we derive our results following two independent approaches, namely, using the solution provided by the Bethe ansatz and the solution provided by an algebraic method, where the electronic operators are represented in a slave-fermion picture. We find that, in the U=\infty case, the finite-temperature charge stiffness is finite for electronic densities, n, smaller than one. These results are essencially those of spinless fermions in a lattice of size L, apart from small corrections coming from a statistical flux, due to the spin degrees of freedom. Up to order t, the Mott-Hubbard gap is \Delta_{MH}=U-4t, and we find that D(T) is finite for n<1, but is zero at half-filling. This result comes from the effective flux felt by the holon excitations, which, due to the presence of doubly occupied sites, is renormalized to \Phi^{eff}=\phi(N_h-N_d)/(N_d+N_h), and which is zero at half-filling, with N_d and N_h being the number of doubly occupied and empty lattice sites, respectively. Further, for half-filling, the current transported by any eigenstate of the system is zero and, therefore, D(T) is also zero.

Anomalous flux quantization in a hubbard ring with correlated hopping.

We solve exactly a generalized Hubbard ring with twisted boundary conditions. The magnitude of the nearest-neighbor hopping depends on the occupations of the sites involved and the term which modifies the number of doubly occupied sites ${t}_{\mathrm{AB}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$. Although $\ensuremath{\eta}$-pairing states with off-diagonal long-range order are part of the degenerate ground state, the behavior of the energy as a function of the twist rules out superconductivity in this limit. A small ${t}_{\mathrm{AB}}$ breaks the degeneracy and for moderate repulsive $U$ introduce superconducting correlations which lead to ``anomalous'' flux quantization.

Finite-size effects and unsaturated ferromagnetism of two-component Hubbard rings in a strong magnetic field: Exact results

We consider two-component Hubbard models in a strong magnetic field to reveal finite-size effects in the stability of the fully polarized state against one- and two-spin flips. Also established are the criteria for unsaturated ferromagnetism, with ${\mathit{S}}_{\mathrm{max}}$ and ${\mathit{S}}^{\mathit{z}}$ reduced, depending on the relative signs of hopping parameters. The behavior of the critical field for periodic chains with arbitrary length at half filling is driven by Coulomb interaction, lattice frustration, and crucially band curvature. Unsaturated ferromagnetism, reminiscent of Nagaoka-like behavior, and the influence of spin liquid states are examined in the structure of off-diagonal spin correlations at large U. \textcopyright{} 1996 The American Physical Society.

Renormalization group and exact diagonalization studies of Hubbard rings with impurities.

We studied mesoscopic Hubbard rings with impurities using the renormalization group (RG) technique and the exact diagonalizations. The exact diagonalization calculations showed that the charge stiffness normalized by the value of a clean system has a peak as a function of electron-electron interactions. Previous RG analysis has succeeded in showing the enhancement of the stiffness at weak interactions, but does not reveal the peak behavior. We derived RG equations with a 4${\mathit{k}}_{\mathit{F}}$ impurity scattering term, which was ignored in the previous studies, and reproduced the overall behavior of the exact diagonalization results. \textcopyright{} 1996 The American Physical Society.

Fine structure and fractional M/N Aharonov-Bohm effect.

We find a fine structure in the Aharonov-Bohm effect, characterized by the appearence of a new type of periodic oscillations having smaller fractional period and an amplitude, which may compare with the amplitude of the conventional Aharonov-Bohm effect. Specifically, at low density or strong coupling on a Hubbard ring can coexist along with the conventional Aaronov-Bohm oscillations with the period equal to an integer, measured in units of the elementary flux quantum, two additional oscillations with periods $1/N$ and $M/N$. The integers $N$ and $M$ are the particles number and the number of down-spin particles, respectively. {}From a solution of the Bethe ansatz equations for $N$ electrons located on a ring in a magnetic field we show that the fine structure is due to electron-electron and Zeeman interactions. Our results are valid in the dilute density limit and for an arbitrary value of the Hubbard repulsion $U$

Enhanced charge and spin currents in the one-dimensional disordered mesoscopic Hubbard ring.

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 {\em 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.

Effects of geometric Berry phase on persistent currents in large-U one-dimensional Hubbard rings.

Effects of geometric Berry phase on persistent currents in large-U one-dimensional Hubbard rings.

Single-particle spectral density of the Hubbard model.

We calculate the single-particle spectral function for the Hubbard model within the framework of a projection technique equivalent to the two-pole approximation. We show that the two-pole approximation can be well understood as an average characterization of the upper and the lower Hubbard bands, rather than describing a dispersive quasiparticle. By comparing with numerical spectra of finite Hubbard rings and of a 4\ifmmode\times\else\texttimes\fi{}4 cluster [P. W. Leung et al., Phys. Rev. B 46, 11 779 (1992)], we show that the present approximation is capable of reproducing essential properties of the single-particle spectral function. In particular, the two-pole spectrum is characterized by a direct gap, in agreement with the exact spectrum. We emphasize the role of local antiferromagnetic correlations.

Quantum fluctuations in the one dimensional Hubbard model with a less than half filling

The electronic structure of the one dimensional Hubbard model with a less than half filling is studied by the resonating Hartree-Fock (Res HF) method. For the Hubbard ring with 16 sites, the Res HF wave function composed of only 6 Slater determinants can explain at most 98.6% (14 electrons) and 99.4% (10 electrons) of the exact correlation energy. The spin structure factor in the Res HF ground state has a cusp at Q = 2 pF, which is consistent with the previous quantum Monte CArlo result.