Self-Consistent Projection Operator Theory for Quantum Many-Body Systems

TL;DR

This paper introduces an exact, efficient projection operator-based method for analyzing quantum many-body systems, extending mean-field and open quantum systems theories with high accuracy for complex dynamics.

Contribution

It develops a self-consistent projection operator theory providing a new analytical framework for quantum many-body dynamics applicable to various lattice systems.

Findings

Accurately models unitary evolution of non-equilibrium states

Effectively describes stationary states in driven-dissipative systems

Offers a systematic extension of mean-field and open quantum systems approaches

Abstract

We derive an exact equation of motion for the reduced density matrices of individual subsystems of quantum many-body systems of any lattice dimension and arbitrary system size. Our projection operator based theory yields a highly efficient analytical and numerical approach. Besides its practical use it provides a novel interpretation and systematic extension of mean-field approaches and an adaption of open quantum systems theory to settings where a dynamically evolving environment has to be taken into account. We show its high accuracy for two significant classes of complex quantum many-body dynamics, unitary evolutions of non-equilibrium states in closed and stationary states in driven-dissipative systems.