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International Journal of Modern Physics B

Nonlinear entangled quantum dynamics in many-body systems with strong electron correlation

Jongbae Hong

Published Mar 3, 2017• 1 citation
Publisher

Abstract

A quantum impurity system out of equilibrium comprises two metallic reservoirs with different chemical potentials and one mediating spin impurity between them. We study the highly nonlinear tunneling conductance of this system, and clarify that three coherent peaks, one zero-bias peak and two side peaks, naturally appear in the tunneling conductance. We use the Liouvillian approach, in which a complete set of basis operators is available, and construct a Liouville matrix to obtain Green’s function at the mediating site. We show that the two coherent side peaks are the outcome of steady-state nonequilibrium combined with strong electron correlation at the mediating site. Tunneling in the quantum impurity system out of equilibrium is performed by an entangled state which is a linear combination of two Kondo singlets formed by the spin at the mediating site and the coherent spins in each reservoir. The fluctuation by incoherent spins is also included. The spectral weights and positions of the three coherent peaks are analytically discussed via atomic limit analysis. Our theoretical results well fit experimental data obtained for quantum point contacts with symmetric and asymmetric Kondo couplings.

DOI
10.1142/s0217979217420097

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A quantum impurity system out of equilibrium comprises two metallic reservoirs with different chemical potentials and one mediating spin impurity between them. We study the highly nonlinear tunneling conductance of this system, and clarify that three coherent peaks, one zero-bias peak and two side peaks, naturally appear in the tunneling conductance. We use the Liouvillian approach, in which a complete set of basis operators is available, and construct a Liouville matrix to obtain Green’s function at the mediating site. We show that the two coherent side peaks are the outcome of steady-state nonequilibrium combined with strong electron correlation at the mediating site. Tunneling in the quantum impurity system out of equilibrium is performed by an entangled state which is a linear combination of two Kondo singlets formed by the spin at the mediating site and the coherent spins in each reservoir. The fluctuation by incoherent spins is also included. The spectral weights and positions of the three coherent peaks are analytically discussed via atomic limit analysis. Our theoretical results well fit experimental data obtained for quantum point contacts with symmetric and asymmetric Kondo couplings.
We clarify the difference between entangled and nonentangled two-reservoir mesoscopic Kondo systems and reveal the reason why theories using the Keldysh formalism, quantum Monte Carlo calculations, and the renormalization group approaches cannot explain the line shapes of tunneling conductance of mesoscopic Kondo systems measured by using a two-terminal setup but explain those of a three-terminal setup. We emphasize that the previous theories study a nonentangled system, while real two-reservoir mesoscopic Kondo systems are entangled systems in which two reservoirs are within the coherent region. We show that two coherent side peaks appearing in tunneling conductance signify the entanglement between two reservoirs. These side peaks are essential for explaining the experimental observations for tunneling conductance.
A systematic study is performed on time-dependent dynamic transport characteristics of a side-coupled double-quantum-impurity system based on the hierarchical equations of motion. It is found that the transport current behaves like a single quantum dot when the coupling strength is low during tunneling or Coulomb coupling. For the case of only tunneling transition, the dynamic current oscillates due to the temporal coherence of the electron tunneling device. The oscillation frequency of the transport current is related to the step voltage applied by the lead, while temperature T, electron–electron interaction U and the bandwidth W have little influence. The amplitude of the current oscillation exists in positive correlation with W and negative correlation with U. With the increase in coupling t 12 between impurities, the ground state of the system changes from a Kondo singlet of one impurity to a spin singlet of two impurities. Moreover, lowering the temperature could promote the Kondo effect to intensify the oscillation of the dynamic current. When only the Coulomb transition is coupled, it is found that the two split-off Hubbard peaks move upward and have different interference effects on the Kondo peak at the Fermi surface with the increase in U 12, from the dynamics point of view.
We develop a nonperturbative dynamical theory (NDT) to calculate the retarded Green's function under nonequilibrium conditions. The NDT is particularly useful for treating nonequilibrium transport problems in systems with strong correlation. We apply our NDT to the well-known single-impurity Anderson model at equilibrium to determine its feasibility. We then apply it to a nonequilibrium transport problem in a system with Kondo coupling. An Anderson model with two metallic reservoirs is studied to understand the phenomenon of Kondo-peak splitting in a single-electron transistor of mesoscopic size. We calculate the nonequilibrium retarded Green's function by using the NDT and analyze it in the atomic limit, where the novel coherent phenomenon manifested only under nonequilibrium conditions can be described in an analytical manner. We finally construct a self-consistent loop to calculate the retarded Green's function and present the results for spectral density and differential conductance obtained by the self-consistent method. Our results explain all the features of Kondo-peak splitting observed in experiments. One remarkable conclusion is that Kondo-peak splitting is not the splitting of a conventional Kondo peak, but the splitting of a novel coherent peak created under nonequilibrium steady-state conditions.
We investigate nonlinear thermoelectric transport through quantum impurity systems with strong on-site interactions. We show that the steady-state transport through interacting quantum impurities in contact with electron reservoirs at significantly different temperatures can be captured by an effective-equilibrium density matrix, expressed compactly in terms of the Lippmann-Schwinger operators of the system. In addition, the reservoirs can be maintained at arbitrary chemical potentials. The interplay between the temperature gradient and bias voltage gives rise to a nontrivial breaking of particle-hole symmetry in the strongly correlated regime, manifest in the Abrikosov-Suhl localized electron resonance. This purely many-body effect, which is in agreement with experimental results, is beyond the purview of mean-field arguments.
We study the steady-state entanglement and correlations of an open system comprising two coupled fermions in the equilibrium or nonequilibrium environments and distill the nonequilibrium contribution to the quantum correlations. We show that in the equilibrium condition, the steady-state quantum correlations exhibit nonmonotonic behavior, while in the nonequilibrium case, the monotonicity is determined by many parameters. The entanglement vanishes abruptly upon the increase of the temperature (bias) and chemical potential bias, and it witnesses a critical chemical potential above which the concurrence always remains positive. In the fermionic reservoirs, quantum correlations reach the maximal values when one chemical potential of the reservoirs matches the system frequency. We separate the quantum correlation generation due to the averaged effect from the pure nonequilibrium effect. In contrast with previous results, when the averaged effect is separated out, the nonequilibrium generation of quantum correlation shows a distinctive monotonic behavior. The difference between the large-tunneling regime with decaying correlations and the small-tunneling with increasing correlations is discussed. Near the boundary of the two regimes, the entanglement behavior is a mixture of two extremes, and it resurrects with the increase of chemical potential bias after its previous drop to zero.
Semiconductor double‐quantum dots represent an ideal system for studying the novel spin physics of localized spins. On each quantum dot when the number of electrons is odd and the net spin is 1/2, a strong coupling of this localized spin to conducting electrons in the leads gives rise to Kondo correlation. On the other hand, in the coupled double‐quantum‐dot if the inter‐dot antiferromagnetic interaction is strong, the two spins can form a correlated spin‐singlet state, quenching the Kondo effect. This competition between Kondo and antiferromagnetic correlation is studied in a controlled manner by tuning the inter‐dot tunnel coupling. Increasing the inter‐dot tunneling, we observe a continuous transition from a single‐peaked to a double‐peaked Kondo resonance in the differential conductance. On the double‐peaked side, the differential conductance becomes suppressed at zero source‐drain bias. The observed strong suppression of the differential conductance at zero bias provides direct evidence signaling the formation of an entangled spin‐singlet state. This evidence for entanglement and the tunability of our devices bode well for quantum computation applications.