Topology in out of equilibrium strongly correlated systems

Project Information

NonequilibriumAnyons

Grant agreement ID: 893915

DOI

10.3030/893915

Project closed

EC signature date 20 April 2020

Start date 19 April 2021

End date 30 March 2024

Funded under

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Total cost

€ 212 933,76

EU contribution

€ 212 933,76

Coordinated by

THE CHANCELLOR MASTERS AND SCHOLARS OF THE UNIVERSITY OF CAMBRIDGE
United Kingdom

Periodic Reporting for period 1 - NonequilibriumAnyons (Topology in out of equilibrium strongly correlated systems)

Reporting period: 2021-04-19 to 2023-04-18

Summary of the context and overall objectives of the project

The synergy of topology and physics has revolutionized how we understand and classify matter in recent decades. By bringing concepts from an abstract mathematical realm of topology, it has been shown that quantum mechanical wave functions can tie knots and do twists in the abstract spaces they live in. Most importantly, these abstract knots and twists come to life as observables in the form of perfectly quantized integer or fractional responses. These topological properties are extremely robust, and hence, even constitute promising candidates for advanced electronics and fault-tolerant quantum computation schemes. Topological systems involving non-Abelian braiding offer more exotic properties, where doing two chosen operations in different orders result in different effects. Characterization and experimental observation of such topologies are active fields of research in conventional materials as well as in state-of-the-art quantum simulators which are artificial systems cleverly designed to simulate these quantum phenomena. At this junction, this project has considered settings beyond equilibrium since life is dynamic and our technology relies on non-equilibrium physics. We have investigated out-of-equilibrium dynamics and classification of topological systems, unearthed novel robust responses far from equilibrium and explored how to harness these properties in laboratories. We have discovered new topological phases where electrons perform a precise dance to realize these non-Abelian properties which cannot exists in a static context.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

The work performed centered around investigating non-equilibrium and dynamical response of topological systems, which can feature intriguing non-Abelian properties, while aiming also at exploring various signatures for these exotic topological phases and their realization in laboratories. This involved considering systems driven out of equilibrium by periodic driving or sudden changes in system parameters, where we constructed relevant models in various settings and employed analytical and numerical calculations to characterize them. Main results have been the retrieval of this novel theoretical knowledge which have been accordingly reported in 8 publications in top-tier journals and have been also disseminated in a wide range of settings, including two dozen invited talks to present these results to audiences as broad as possible.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

The results of the project have been presented in 8 publications and have been disseminated in numerous invited talks to a wide range of audiences, underpinning the impact and broad-reach of these research results. Since this is a project concerning fundamental theoretical research, the innovative nature lies at the new topological phenomena, phases and probes discovered. Identified possible connections are reported in these publications, which in turn can aid future developments of new quantum technologies by their nature. In particular, in one article published in Nature Communications, we reported on a new novel type of topology with no static counterpart (see attached illustration). This has attracted great attention since they can only arise via non-Abelian braiding and out of equilibrium under periodic driving such as under a laser light.

braiding.png