Fermionic duality: General symmetry of open systems with strong  dissipation and memory

Bruch, Valentin; Nestmann, K.; Schulenborg, Jens; Wegewijs, M. R.

doi:10.21468/scipostphys.11.3.053

Cited by 9 publications

(31 citation statements)

References 95 publications

(310 reference statements)

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“…3 Renormalized perturbation theory around T = ∞ With these ideas in mind, we now concretely set up the approach for the Anderson impurity model, noting that the following analysis can be extended straightforwardly to a large class of relevant fermionic models, see Refs. [23,25,27] for details. The system consists of a single orbital quantum dot with energy ε and Coulomb repulsion U described by…”

Section: Temperature As Flow Parameter: Time-correlationsmentioning

confidence: 99%

“…( 29) requires the temperature derivative of the effective supervertex ∂ T G 1 . It can be obtained by differentiating (27). Here the two-point vertex ∂ T G 12 enters, which can only be expressed in an exact manner using three-point vertices ∂ T G 123 and so on.…”

Section: The T -Flow Renormalization Groupmentioning

confidence: 99%

“…This led on the one hand to the discovery of the non-perturbative fermionic duality [25,26], an exact "dissipative symmetry" which cross-relates different eigenvalues and -vectors of the memory kernel and propagator in a simple fashion. Corresponding exact relations for the Kraus measurement operators of the dynamics, the time-local generator and its Lindblad jump rates and -operators have recently been worked out [27]. On the other hand, it was found that approximate calculations could be improved beyond the standard bare perturbation theory [28,29]: by directly going to the wideband limit a much simplified renormalized perturbation series was obtained [6,22,23,30].…”

Section: Introductionmentioning

confidence: 99%

“…Unlike the bare expansion around the decoupled limit Γ → 0 of reversible dynamics, here one expands around the high-temperature limit T → ∞, which already includes dissipative behavior into the reference solution of the series. This leads to completely differentand often better behaved -memory-kernel approximations [6,22,23,30] and facilitates solution of exactly solvable cases [23,27,30].…”

Section: Introductionmentioning

confidence: 99%

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Renormalization group for open quantum systems using environment temperature as flow parameter

Nestmann,

Wegewijs

2021

Preprint

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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. In the stationary limit, readily accessible in real-time for voltages on the order of the coupling or larger, we benchmark 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 behavior when the metallic reservoirs have a flat wide band.

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Section: Temperature As Flow Parameter: Time-correlationsmentioning

confidence: 99%

Section: The T -Flow Renormalization Groupmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Renormalization group for open quantum systems using environment temperature as flow parameter

Nestmann,

Wegewijs

2021

Preprint

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“…We analyze the full thermoelectric response of the quantum dot using expressions obtained from a recently established, general fermionic duality 16,19,25,28 . This purely dissipative symmetry, applied to a weak-coupling master-equation description, maps the transport dynamics of fermionic open non-equilibrum systems to those of dual systems with signinverted local energies, chemical potentials, and energydependencies of the tunnel couplings:…”

mentioning

confidence: 99%

Thermovoltage in quantum dots with attractive interaction

Schulenborg

Wegewijs

Splettstoesser

2020

Applied Physics Letters

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We study the linear and nonlinear thermovoltage of a quantum dot with effective attractive electron-electron interaction and weak, energydependent tunnel coupling to electronic contacts. Remarkably, we find that the thermovoltage shows signatures of repulsive interaction, which can be rationalized. These thermovoltage characteristics are robust against large potential and temperature differences well into the nonlinear regime, which we expect can be demonstrated in current state-of-the-art experiments. Furthermore, under nonlinear operation, we find extended regions of large power production at efficiencies on the order of the Curzon-Ahlborn bound interrupted only by a characteristic sharp dip.

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Extracting dynamical maps of non-Markovian open quantum systems

Strachan,

Purkayastha,

Clark

2024

The Journal of Chemical Physics

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The most general description of quantum evolution up to a time τ is a completely positive tracing preserving map known as a dynamical mapΛ̂(τ). Here, we consider Λ̂(τ) arising from suddenly coupling a system to one or more thermal baths with a strength that is neither weak nor strong. Given no clear separation of characteristic system/bath time scales, Λ̂(τ) is generically expected to be non-Markovian; however, we do assume the ensuing dynamics has a unique steady state, implying the baths possess a finite memory time τm. By combining several techniques within a tensor network framework, we directly and accurately extract Λ̂(τ) for a small number of interacting fermionic modes coupled to infinite non-interacting Fermi baths. First, we use an orthogonal polynomial mapping and thermofield doubling to arrive at a purified chain representation of the baths whose length directly equates to a time over which the dynamics of the infinite baths is faithfully captured. Second, we employ the Choi–Jamiolkowski isomorphism so that Λ̂(τ) can be fully reconstructed from a single pure state calculation of the unitary dynamics of the system, bath and their replica auxiliary modes up to time τ. From Λ̂(τ), we also compute the time local propagator L̂(τ). By examining the convergence with τ of the instantaneous fixed points of these objects, we establish their respective memory times τmΛ and τmL. Beyond these times, the propagator L̂(τ) and dynamical map Λ̂(τ) accurately describe all the subsequent long-time relaxation dynamics up to stationarity. These timescales form a hierarchy τmL≤τmΛ≤τre, where τre is a characteristic relaxation time of the dynamics. Our numerical examples of interacting spinless Fermi chains and the single impurity Anderson model demonstrate regimes where τre ≫ τm, where our approach can offer a significant speedup in determining the stationary state compared to directly simulating the long-time limit. Our results also show that having access to Λ̂(τ) affords a number of insightful analyses of the open system thus far not commonly exploited.

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Fermionic duality: General symmetry of open systems with strong dissipation and memory

Cited by 9 publications

References 95 publications

Renormalization group for open quantum systems using environment temperature as flow parameter

Renormalization group for open quantum systems using environment temperature as flow parameter

Thermovoltage in quantum dots with attractive interaction

Extracting dynamical maps of non-Markovian open quantum systems

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