Diffusive modes of two-band fermions under number-conserving dissipative dynamics

TL;DR

This paper demonstrates the existence of diffusive modes in a two-band fermionic system under number-conserving dissipative dynamics, revealing how dissipation influences diffusion and complicates state engineering.

Contribution

It explicitly shows diffusive modes in a number-conserving dissipative two-band fermion model, extending previous work and analyzing how dissipation affects diffusion coefficients.

Findings

Diffusive modes exist in the studied dissipative two-band fermion system.

Diffusion coefficient depends on model parameters and dissipation rate.

Diffusive modes impact the engineering of many-body correlated states.

Abstract

Driven-dissipative protocols are proposed to control and create nontrivial quantum many-body correlated states. Protocols conserving the number of particles stand apart. As well-known, in quantum systems with the unitary dynamics the particle number conservation and random scattering yield diffusive behavior of two-particle excitations (diffusons and cooperons). Existence of diffusive modes in the particle-number-conserving dissipative dynamics is not well studied yet. We explicitly demonstrate the existence of diffusons in a paradigmatic model of a two-band system, with dissipative dynamics aiming to empty one fermion band and to populate the other one. The studied model is generalization of the model introduced in F. Tonielli, J. C. Budich, A. Altland, and S. Diehl, Phys. Rev. Lett. 124, 240404 (2020). We find how the diffusion coefficient depends on details of a model and the rate of dissipation. We discuss how the existence of diffusive modes complicates engineering of macroscopic many-body correlated states.