Iterative construction of conserved quantities in dissipative nearly integrable systems

TL;DR

This paper introduces an iterative method to construct conserved quantities in dissipative nearly integrable quantum systems, enabling better understanding and modeling of their stationary states under weak coupling to baths.

Contribution

The authors develop a novel iterative scheme to identify conserved quantities in driven dissipative nearly integrable systems, facilitating efficient thermodynamic calculations.

Findings

Scheme effectively constructs conserved quantities in large systems

Enables truncated generalized Gibbs ensemble descriptions

Provides a pathway to discover unknown conserved quantities

Abstract

Integrable systems offer rare examples of solvable many-body problems in the quantum world. Due to the fine-tuned structure, their realization in nature and experiment is never completely accurate, therefore effects of integrability are observed only transiently. One way to overcome this limitation is to weakly couple nearly integrable systems to baths and driving: these will stabilize integrable effects up to arbitrary time and encode them in the stationary state approximated by a generalized Gibbs ensemble. However, the description of such driven dissipative nearly integrable models is challenging and no exact analytical methods have been proposed so far. Here, we develop an iterative scheme in which integrability breaking perturbations (baths) determine the conserved quantities that play the leading role in a highly efficient truncated generalized Gibbs ensemble description. Our scheme paves the way for easier calculations in thermodynamically large systems and can be used to construct unknown conserved quantities.