Spectral Density Modulation and Universal Markovian Closure of Fermionic Environments

TL;DR

This paper introduces a spectral density modulation technique to simplify fermionic environments and presents a Markovian closure method that reduces computational complexity in simulating open quantum systems with structured fermionic baths.

Contribution

It proposes a spectral density modulation for simplifying fermionic environments and derives a Markovian closure that reduces computational complexity in chain-mapping simulations.

Findings

Spectral density modulation replaces complex fermionic environments with simpler equivalents.

Markovian closure mimics a continuum of bath modes with a small set of damped fermionic modes.

Polynomial reduction in time complexity for long-time dynamics simulations.

Abstract

The combination of chain-mapping and tensor-network techniques provides a powerful tool for the numerically exact simulation of open quantum systems interacting with structured environments. However, these methods suffer from a quadratic scaling with the physical simulation time, and therefore they become challenging in the presence of multiple environments. This is particularly true when fermionic environments, well-known to be highly correlated, are considered. In this work we first illustrate how a thermo-chemical modulation of the spectral density allows replacing the original fermionic environments with equivalent, but simpler, ones. Moreover, we show how this procedure reduces the number of chains needed to model multiple environments. We then provide a derivation of the fermionic Markovian closure construction, consisting of a small collection of damped fermionic modes undergoing a Lindblad-type dynamics and mimicking a continuum of bath modes. We describe, in particular, how the use of the Markovian closure allows for a polynomial reduction of the time complexity of chain-mapping based algorithms when long-time dynamics are needed.