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

TL;DR

This paper reveals a fundamental fermionic duality symmetry in open quantum systems with strong interactions and dissipation, enabling new analytical insights across various quantum dynamic approaches.

Contribution

It introduces a novel fermionic duality relation connecting state and observable evolution, applicable to multiple quantum dynamics frameworks.

Findings

Duality simplifies analytical calculations of fermionic open systems.

Insights into the causal and divisibility structure of fermionic dynamics.

Predictions for fermionic models are more constrained by fundamental principles than previously understood.

Abstract

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.