The role of repulsive on-site and nearest-neighbor Coulomb interactions in disordered half-filled Aharanov-Bohm rings is studied by world-line quantum Monte Carlo simulations. The diverse dependence of the equilibrium persistent current on the couplings is found to relate systematically to the magnetic phase of the model: the maximum charge stiffness (or the persistent current) coexists with the phase-transition line between the dominant charge-density-wave state and the dominant spin-density-wave state. The stiffness vanishes with an increasing departure from the transition line. Thus in the disordered rings the Coulomb interactions can enhance the charge stiffness over the noninteracting limit in such a way as to drive the system toward the phase-transition regime. \textcopyright{} 1996 The American Physical Society.
Recent interest in the fundamental physics of the Kondo effect has been driven by the observation of Kondo physics in mesoscopic systems such as quantum dots [1, 2] and carbon nanotubes [3], which can act analogously to magnetic impurities in a bulk metal. Highly tunable mesoscopic systems such as these present the possibility of observing the controversial Kondo length scale εK associated with the cloud of conduction electrons that screen the spin of the impurity [4]. This plays a similar role in scaling theories as the Kondo temperature Tk. One proposal [5] for detecting this length scale is to measure the finite-size dependence of persistent currents in an isolated conducting ring coupled to a quantum dot. The screening cloud should be 'trapped' in the closed system, and will not form if the size of the ring L is much smaller than εK. In particular, the current in the Kondo regime should be a universal scaling function j = L^-1 f(Φ, L/εK, T/Tk) (here Φ is the applied flux) [6, 7]. Considerable disagreement has arisen in the theoretical estimates of these persistent currents as different analytical treatments yield contradictory predictions [6, 8, 9, 10]. This thesis presents a new Quantum Monte Carlo (QMC) technique for measuring persistent currents in such systems, based on the Hirsch-Fye Impurity QMC algorithm [11] which is ideally suited to treating systems with a single impurity such as the quantum dot. The algorithm provides exact numerical results at finite temperatures. The complexity of the algorithm does not scale directly with the size of the system, making it particularly attractive for investigating a wide range of system sizes.
Aharonov–Bohm physics at the two-particle level is investigated for distinguishable interacting charged particles through the exact solution of a toy model with confined states. The effect of the inaccessible magnetic flux is distributed between the center-of-mass and the internal pair level, and the nontrivial manner in which the two levels mutually affect each other demonstrates the interplay between interactions, the nontrivial topology, the Aharonov–Bohm flux and the characteristics of a charged quantal mixture. Analytical expressions for energy spectra, wavefunctions, (flux-dependent) critical interactions for binding and current densities are derived, and these offer the rare possibility of studying persistent currents from the point of view of an interacting nanoscopic system. Two cyclic adiabatic processes are identified, one coupled to the center-of-mass behavior and the other defined on the two-body interaction potential, with the associated Berry's phases also analytically determined; these are found to be directly linked to the electric and probability (persistent) currents in nontrivial ways that are shown to be universal (independent of the actual form of the interaction). The direct connection of the two-body Berry's phase to the electric current for a neutral system is found to disappear in the case of identical particles—hence revealing the character of a charged mixture as being crucial for exhibiting this universal behavior.
We study the persistent current of correlated spinless electrons in a continuous one-dimensional ring with a single weak link. We include correlations by solving the many-body Schrodinger equation for several tens of electrons interacting via the short-ranged pair interaction V(x - x'). We solve this many-body problem by advanced configuration-interaction (CI) and diffusion Monte Carlo (DMC) methods. Our CI and DMC results show, that the persistent current (I) as a function of the ring length (L) exhibits for large L the power law typical of the Luttinger liquid,
I∝L−1−α, where the power
α depends only on the electron-electron (e-e) interaction. For strong e-e interaction the previous theories predicted for
α the formula
α=(1+2αRG)1/2−1, where
αRG=[V(0)−V(2kF)]/2πℏvF is the renormalisation-group result for weakly interacting electrons, with V(q) being the Fourier transform of V(x-x'). Our numerical data show that this theoretical result holds in the continuous model only if the range of V(x - x') is small (roughly
d≲1/2kF, more precisely
4d2kF2<<1). For strong e-e interaction (
αRG>0.25) our CI data show the power law
I∝L−1−α already for rings with only ten electrons, i.e., ten electrons are already enough to behave like the Luttinger liquid. The DMC data for
αRG>0.25 are damaged by the so-called fixed-phase approximation. Finally, we also treat the e-e interaction in the Hartree-Fock approximation. We find the exponentially decaying I(L) instead of the power law, however, the slope of log(I(L)) still depends solely on the parameter
αRG as long as the range of V(x - x') approaches zero.
Charge persistent currents in single-channel ballistic rings are investigated in various models of strongly correlated electrons (Wigner crystal, Luttinger liquid, Hubbard model, t–J model, and the fermion representation of the Heisenberg–Ising model). The primary objective of the survey is to compare the properties of Aharonov–Bohm oscillations for weakly and strongly correlated electrons and to formulate a set of persistent current characteristics that will unambiguously support the anomalous (departing from a Fermi liquid) behavior of one-dimensional electron systems. For this purpose the onset of the parity effect (dependence of the system response on whether the number of particles in the ring is odd or even) and various properties of the persistent current are analyzed in detail for model spinless fermions and real electrons. The influence of solitary impurities on the value and temperature dependence of the amplitude of the Aharanov–Bohm oscillations is also investigated. It is shown that the formation of a Wigner crystal (which is possible for weakly shielded Coulomb interaction) leads to a very pronounced anomalous (nonmonotonic) temperature dependence of the current in a nonideal ring. The properties of the charge current near the Mott metal–insulator transition are altered to the greatest degree by local types of electron–electron interaction.
We study quantum wires and point contacts with a fixed-node path integral Monte Carlo technique. The fixed-node technique uses a variational principle to map fermionic problems into effective bosonic problems, which are then evaluated with standard quantum Monte Carlo techniques. While fixed-node is an approximation, it has the useful properties of being variational and being able to recover the exact answer when the exact nodes or phases of the density matrix are known. In these finite-temperature simulations we use the free particle density matrix as a fixed-node constraint to efficiently simulate hundreds of interacting electrons. We have calculated charge densities, pair correlation functions, and the currentcurrent Matsubura Green's functions for quantum wires and quantum point contacts.