We extend the imaginary-time formulation of the equilibrium quantum many-body theory to steady-state nonequilibrium with an application to strongly correlated transport. By introducing Matsubara voltage, we keep the finite chemical potential shifts in the Fermi-Dirac function, in agreement with the Keldysh formulation. The formulation is applied to strongly correlated transport in the Kondo regime using the quantum Monte Carlo method.PACS numbers: 73.63. Kv, 72.10.Bg, 72.10.Di A coherent formulation of equilibrium and nonequilibrium is one of the ultimate goals of statistical physics. In the last two decades, this has become a particularly pressing issue with the advances in nanoelectronics. Although it has long been considered such Gibbsian description may exist in the steady-state nonequilibrium [1], implementation of time-independent nonequilibrium quantum statistics has produced limited success [2] without widely applicable algorithms.In nanoelectronics, the strong interplay between manybody interactions and nonequilibrium demands nonperturbative treatments of the quantum many-body effects. Perturbative Green function techniques [3,4] have been successful, but are often plagued by complicated diagrammatic rules and are limited to simple models. In the last few years, important advances have been made in this field to complement the diagrammatic theory. Timedependent renormalization group [5,6] and densitymatrix renormalization group method [7] were applied to calculate the real-time convergence toward the steadystate. Real-time methods [5,6,7] calculate the process toward the steady-state and therefore have clear physical interpretations. Unfortunately they often suffer from long-time behaviors associated with low energy strongly correlated states and finite size effects. Direct construction of nonequilibrium ensembles through the scattering state formalism [2,8,9, 10] and field theoretic approach [11] have provided new perspectives to the problem.The main goal of this work is to provide a critical step toward the time-independent description of equilibrium and steady-state nonequilibrium quantum statistics. In addition to the resolution of this fundamental problem, we provide a strong application. The steadystate nonequilibrium can be solved within the same formal structure as equilibrium, and therefore the powerful equilibrium many-body tools, such as the quantum Monte Carlo (QMC) method, can be easily applied to complex transport systems with many competing interactions. We demonstrate this point by applying this formalism to strongly correlated transport in the Kondo regime by using QMC. In contrast to the real-time methods, this approach starts from the steady-state and simulates the effect of many-body interaction. However, numerical analytic continuation and low temperature calculation, especially with the QMC application, are technical difficulties.In the following, we first construct a time-independent statistical ensemble of steady-state nonequilibrium [2] in the non-interacting limit with the i...

We show that a strongly correlated quantum dot embedded in an Aharonov-Bohm interferometer can be used to filter both charge and spin at zero voltage bias. The magnitude with which the Aharonov-Bohm arm is coupled to the system controls the many-body effects on the quantum dot. When the quantum dot is in the Kondo regime, the flow of charge through the system can be tuned by the phase of the Aharonov-Bohm arm, AB . Furthermore, when a spin-orbit interaction is present on a Kondo quantum dot, we can control the flow of spin by the spin-orbit phase, SO . The existence of the Kondo peak at the Fermi energy makes it possible to control the flow of both charge and spin in the zero voltage bias limit.

A model for nonequilibrium dynamical mean-field theory is constructed for the infinite-dimensional Hubbard lattice. We impose nonequilibrium by expressing the physical orbital as a superposition of a left ͑L͒-moving and right ͑R͒-moving electronic state with the respective chemical potentials L and R . Using the second-order iterative perturbation theory we calculate the quasiparticle properties as a function of the chemical potential bias between the L and R movers, i.e., ⌽ = L − R . The evolution of the nonequilibrium quasiparticle spectrum is mapped out as a function of the bias and temperature. The quasiparticle states with the renormalized Fermi-energy scale QP 0 disappear at ⌽ ϳ QP 0 in the low-temperature limit. The second-order perturbation theory predicts that in the vicinity of the Mott-insulator transition at the Coulomb-parameter U = U c , there exists another critical Coulomb-parameter U d ͑ϽU c ͒ such that, for U d Ͻ U Ͻ U c , quasiparticle states are destroyed abruptly when ͑ QP 0 ͒ 2 ϳ a͑k B T c ͒ 2 + b⌽ c 2 with the critical temperature T c , the critical bias ⌽ c , and the numerical constants a and b on the order of unity.In recent years significant experimental progress has been made in the fabrication of sophisticated electronic heterostructures utilizing strongly correlated electronic materials. These systems have given rise to the discovery of rich novel phenomena. These include: ballistic transport of electrons through heterostructures of superconductors, 1 ferromagnets, 2 magnetic tunneling junctions, 3,4 and oxides. 5-8 With this vast array of strongly correlated heterostructures it is very important to theoretically understand how the strongly correlated materials in the bulk limit will behave under nonequilibrium conditions. In this work we formulate the nonequilibrium problem in the lattice and present significant progress toward a more complete understanding of strongly correlated lattices out of equilibrium.We are interested in heterostructures of strongly correlated materials under a finite source-drain bias where the voltage drop occurs mainly at the interface of the strongly correlated material and the source/drain leads, as considered previously. 9,10 By this construction this model may not be sufficient to describe nonequilibrium in true-bulk systems. However, we speculate that this model is relevant to nanoscale devices where the nonequilibrium is established by unequal statistics between ballistic electrons from source and drain. This study will give an insight on how the lattice effects manifest in such systems. Our focus here is to investigate the evolution of strongly correlated quasiparticle spectra due to nonequilibrium driven by an imbalance in the chemical potentials. In this work we gain qualitative understanding on how the enhanced dephasing by the new particle-hole decay channel due to nonequilibrium modifies the spectral properties.One of the most practical and powerful theoretical techniques for studying strongly correlated lattices is the dynamical mean-field theo...

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