Random Matrix Ensembles For Many-Body Quantum Systems

TL;DR

This paper reviews embedded random matrix ensembles tailored for quantum many-body systems and demonstrates their effectiveness in modeling decoherence phenomena in qubits interacting with complex environments.

Contribution

It provides an overview of embedded random matrix ensembles and illustrates their application in studying decoherence in quantum systems.

Findings

Decoherence depends on the environment's nature.

Embedded ensembles effectively model many-body quantum interactions.

Numerical results highlight environment influence on decoherence.

Abstract

Classical random matrix ensembles were originally introduced in physics to approximate quantum many-particle nuclear interactions. However, there exists a plethora of quantum systems whose dynamics is explained in terms of few-particle (predominantly two-particle) interactions. The random matrix models incorporating the few-particle nature of interactions are known as embedded random matrix ensembles. In the present paper, we provide a brief overview of these two ensembles and illustrate how the embedded ensembles can be successfully used to study decoherence of a qubit interacting with an environment, both for fermionic and bosonic embedded ensembles. Numerical calculations show the dependence of decoherence on the nature of the environment.