Experimental characterization of quantum many-body localization transition

TL;DR

This paper presents an experimental method using a 12-qubit superconducting array to detect the many-body localization transition, revealing how dynamics sensitivity peaks at the transition and indicating a mobility edge.

Contribution

The study introduces a scalable protocol for identifying the many-body localization transition point through dynamical measurements in superconducting qubits.

Findings

Maximum sensitivity of dynamics at the transition point

Excellent agreement between simulation and experiment

Detection of mobility edge through initial state variation

Abstract

As strength of disorder enhances beyond a threshold value in many-body systems, a fundamental transformation happens through which the entire spectrum localizes, a phenomenon known as many-body localization. This has profound implications as it breaks down fundamental principles of statistical mechanics, such as thermalization and ergodicity. Due to the complexity of the problem, the investigation of the many-body localization transition has remained a big challenge. The experimental exploration of the transition point is even more challenging as most of the proposed quantities for studying such effect are practically infeasible. Here, we experimentally implement a scalable protocol for detecting the many-body localization transition point, using the dynamics of a $N=12$ superconducting qubit array. We show that the sensitivity of the dynamics to random samples becomes maximum at the transition point which leaves its fingerprints in all spatial scales. By exploiting three quantities, each with different spatial resolution, we identify the transition point with excellent match between simulation and experiment. In addition, one can detect the evidence of mobility edge through slight variation of the transition point as the initial state varies. The protocol is easily scalable and can be performed across various physical platforms.