SciPost Phys. 12, 121 (2022) ·
published 7 April 2022
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We present the $T$-flow renormalization group method, which computes the
memory kernel for the density-operator evolution of an open quantum system by
lowering the physical temperature $T$ of its environment. This has the key
advantage that it can be formulated directly in real time, making it
particularly suitable for transient dynamics, while automatically accumulating
the full temperature dependence of transport quantities. We solve the $T$-flow
equations numerically for the example of the single impurity Anderson model. We
benchmark in the stationary limit, readily accessible in real-time for voltages
on the order of the coupling or larger using results obtained by the functional
renormalization group, density-matrix renormalization group and the quantum
Monte Carlo method. Here we find quantitative agreement even in the worst case
of strong interactions and low temperatures, indicating the reliability of the
method. For transient charge currents we find good agreement with results
obtained by the 2PI Green's function approach. Furthermore, we analytically
show that the short-time dynamics of both local and non-local observables
follow a universal temperature-independent behaviour when the metallic
reservoirs have a flat wide band.
Valentin Bruch, Konstantin Nestmann, Jens Schulenborg, Maarten R. Wegewijs
SciPost Phys. 11, 053 (2021) ·
published 10 September 2021
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We consider the exact time-evolution of a broad class of fermionic open quantum systems with both strong interactions and strong coupling to wide-band reservoirs. We present a nontrivial fermionic duality relation between the evolution of states (Schr\"odinger) and of observables (Heisenberg). We show how this highly nonintuitive relation can be understood and exploited in analytical calculations within all canonical approaches to quantum dynamics, covering Kraus measurement operators, the Choi-Jamio{\l}kowski state, time-convolution and convolutionless quantum master equations and generalized Lindblad jump operators. We discuss the insights this offers into the divisibility and causal structure of the dynamics and the application to nonperturbative Markov approximations and their initial-slip corrections. Our results underscore that predictions for fermionic models are already fixed by fundamental principles to a much greater extent than previously thought.
SciPost Phys. 7, 012 (2019) ·
published 25 July 2019
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We study the reduced time-evolution of open quantum systems by combining
quantum-information and statistical field theory. Inspired by prior work [EPL
102, 60001 (2013) and Phys. Rev. Lett. 111, 050402 (2013)] we establish the
explicit structure guaranteeing the complete positivity (CP) and
trace-preservation (TP) of the real-time evolution expansion in terms of the
microscopic system-environment coupling.
This reveals a fundamental two-stage structure of the coupling expansion:
Whereas the first stage defines the dissipative timescales of the system
--before having integrated out the environment completely-- the second stage
sums up elementary physical processes described by CP superoperators. This
allows us to establish the nontrivial relation between the (Nakajima-Zwanzig)
memory-kernel superoperator for the density operator and novel memory-kernel
operators that generate the Kraus operators of an operator-sum. Importantly,
this operational approach can be implemented in the existing Keldysh real-time
technique and allows approximations for general time-nonlocal quantum master
equations to be systematically compared and developed while keeping the CP and
TP structure explicit.
Our considerations build on the result that a Kraus operator for a physical
measurement process on the environment can be obtained by 'cutting' a group of
Keldysh real-time diagrams 'in half'. This naturally leads to Kraus operators
lifted to the system plus environment which have a diagrammatic expansion in
terms of time-nonlocal memory-kernel operators. These lifted Kraus operators
obey coupled time-evolution equations which constitute an unraveling of the
original Schr\"odinger equation for system plus environment. Whereas both
equations lead to the same reduced dynamics, only the former explicitly encodes
the operator-sum structure of the coupling expansion.
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