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arXiv:1907.09546 · Physical review. B./Physical review. B

Numerically exact full counting statistics of the energy current in the Kondo regime

Michael L. Ridley, Michael Galperin, Emanuel Gull, Guy Cohen

Published Oct 16, 2019• 38 citations
arXivHTMLPDF

Abstract

We use the inchworm quantum Monte Carlo method to investigate the full counting statistics of particle and energy currents in a strongly correlated quantum dot. Our method is used to extract the heat fluctuations and entropy production of a quantum thermoelectric device, as well as cumulants of the particle and energy currents. The energy-particle current cross correlations reveal information on the preparation of the system and the interplay of thermal and electric currents. We furthermore demonstrate the signature of a crossover from Coulomb blockade to Kondo physics in the energy current fluctuations, and show how the conventional master equation approach to full counting statistics systematically fails to capture this crossover.

DOI
10.1103/physrevb.100.165127

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We use the inchworm quantum Monte Carlo method to investigate the full counting statistics of particle and energy currents in a strongly correlated quantum dot. Our method is used to extract the heat fluctuations and entropy production of a quantum thermoelectric device, as well as cumulants of the particle and energy currents. The energy-particle current cross correlations reveal information on the preparation of the system and the interplay of thermal and electric currents. We furthermore demonstrate the signature of a crossover from Coulomb blockade to Kondo physics in the energy current fluctuations, and show how the conventional master equation approach to full counting statistics systematically fails to capture this crossover.
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We study the full counting statistics (FCS) of electron tunneling through a multiterminal quantum dot in the Kondo regime within the slave-boson mean-field theory. By employing the method of Gogolin and Komnik for calculating the FCS generating function based on the nonequilibrium Green's function [Phys. Rev. B 73, 195301 (2006)], we obtain the counting field $\ensuremath{\lambda}$-dependent self-consistent equations for the mean values of the slave-boson fields and the explicit expression for the derivative of the adiabatic potential of the system with respect to the counting fields. Performing a perturbative expansion to the first order of $\ensuremath{\lambda}$, we find an extra contribution to the shot noise due to the bias-induced Bose field fluctuation, and then confirm that the nonequilibrium particle number fluctuation plays an important role in the current noise of the Kondo dot: enhancement of the current autocorrelation and a positive current cross-correlation.
We introduce a numerical method to sample the distributions of charge, heat, and entropy production in open quantum systems coupled strongly to macroscopic reservoirs, with both temporal and energy resolution and beyond the linear-response regime. Our method exploits the mesoscopic-leads formulation, where macroscopic reservoirs are modeled by a finite collection of modes that are continuously damped toward thermal equilibrium by an appropriate Gorini-Kossakowski-Sudarshan-Lindblad master equation. Focussing on noninteracting fermionic systems, we access the time-resolved full counting statistics through a trajectory unraveling of the master equation. We show that the integral fluctuation theorems for the total entropy production, as well as the martingale and uncertainty entropy production, hold. Furthermore, we investigate the fluctuations of the dissipated heat in finite-time information erasure. Conceptually, our approach extends the continuous-time trajectory description of quantum stochastic thermodynamics beyond the regime of weak system-environment coupling.
We present a method for calculating the full counting statistics of a nonequilibrium quantum system based on the propagator noncrossing approximation (NCA). This numerically inexpensive method can provide higher-order cumulants for extended parameter regimes, rendering it attractive for a wide variety of purposes. We compare NCA results to Born-Markov quantum master equations (QME) results to show that they can access different physics, and to numerically exact inchworm quantum Monte Carlo data to assess their validity. As a demonstration of its power, the NCA method is employed to study the impact of correlations on higher-order cumulants in the nonequilibrium Anderson impurity model. The four lowest-order cumulants are examined, allowing us to establish that correlation effects have a profound influence on the underlying transport distributions. Higher-order cumulants are therefore demonstrated to be a proxy for the presence of Kondo correlations in a way that cannot be captured by simple QME methods.
We study the thermoelectric performance and stationary quantum correlations of a coherent double quantum dot heat engine driven solely by two conventional electronic reservoirs. The role of coherence is isolated by comparing the fully coherent dynamics with those under an energy-conserving pure dephasing channel that does not alter the system energy. Reducing the dephasing strength enhances the particle current, heat current, output power, and thermodynamic efficiency over a broad voltage range. After optimizing the electrochemical load and the dot energy levels, we find that coherence primarily amplifies the attainable power and efficiency without significantly relocating the optimal operating region. Although appreciable interdot coherence already exists at moderate Coulomb interaction, stationary entanglement emerges only when Coulomb blockade sufficiently suppresses the mixed-state contribution from the empty and doubly occupied states. We further construct a transport-based lower bound on the concurrence, providing an experimentally accessible entanglement witness that avoids full state tomography. These findings establish a clear hierarchy among energy filtering, quantum coherence, and Coulomb blockade in a minimal quantum thermoelectric device.
Recently, a "unified" quantum master equation was derived and shown to be of the Gorini-Kossakowski-Lindblad-Sudarshan form. This equation describes the dynamics of open quantum systems in a manner that forgoes the full secular approximation and retains the impact of coherences between eigenstates close in energy. We implement full counting statistics with the unified quantum master equation to investigate the statistics of energy currents through open quantum systems with nearly degenerate levels. We show that, in general, this equation gives rise to dynamics that satisfy fluctuation symmetry, a sufficient condition for the Second Law of Thermodynamics at the level of average fluxes. For systems with nearly degenerate energy levels, such that coherences build up, the unified equation is simultaneously thermodynamically consistent and more accurate than the fully secular master equation. We exemplify our results for a "V" system facilitating energy transport between two thermal baths at different temperatures. We compare the statistics of steady-state heat currents through this system as predicted by the unified equation to those given by the Redfield equation, which is less approximate but, in general, not thermodynamically consistent. We also compare results to the secular equation, where coherences are entirely abandoned. We find that maintaining coherences between nearly degenerate levels is essential to properly capture the current and its cumulants. On the other hand, the relative fluctuations of the heat current, which embody the thermodynamic uncertainty relation, display inconsequential dependence on quantum coherences.