The localization frontier---from many-body localization to amorphous topological matter via the landscape

Project Information

LOCFRONT

Grant agreement ID: 101001902

DOI

10.3030/101001902

Project closed

EC signature date 27 January 2021

Start date 1 June 2021

End date 31 May 2026

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 815 978,00

EU contribution

€ 1 815 978,00

Coordinated by

KUNGLIGA TEKNISKA HOEGSKOLAN
Sweden

Periodic Reporting for period 3 - LOCFRONT (The localization frontier---from many-body localization to amorphous topological matter via the landscape)

Reporting period: 2024-06-01 to 2025-11-30

Summary of the context and overall objectives of the project

The last decade has seen impressive progress in the control and understanding of closed many-body quantum systems, propelled by the drive towards quantum technology. This progress, especially in understanding nonequilibrium many-body quantum dynamics, is now severely hampered by the limited toolbox available for studying such systems. This is especially true in systems far from their absolute zero temperature ground states and where disorder or imperfections play a crucial role. Such systems are at the core of some of the most fundamental open questions in quantum physics, including how and when such systems become thermal and behave according to classical expectations, and when they do not. The many-body localization transition is a poorly understood, unconventional dynamic phase transition that is believed to prevent many-body quantum systems from thermalizing. The underlying mechanism for this transition is localization of particles due to quantum interference induced by scattering of imperfections. As a result of the localization, quantum information that otherwise would become inaccessible due to thermalization, can in principle be retained indefinitely.

The major objective of this project is to significantly enhance and enlarge the toolbox for study of quantum-many body dynamics and localization physics in general, and by applying the new tools address open fundamental questions about quantum physics. The problem is hard, and most approaches to new tools are at the outset likely to fail. The project therefore takes a multipronged approach by developing several new methods in addition to improving and applying old ones in new directions. This includes conceptually new approaches to localization inspired by recent advances in mathematics, which will be broadly applicable to localization physics in general. This broad applicability will be demonstrated by also applying it to the physics of amorphous topological matter.

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

We have succeeded in adding at least three new and important tools into the toolbox for studying quantum systems. The first one is highlighted by the development of a new algorithm that we have coined LITE, for local information time evolution. The essential idea behind this algorithm is the separation of quantum information (entanglement) into different scales, and the understanding that the details of the large scale information is not essential for local observables. This entanglement can therefore be simplified or discarded, allowing for simulations of many-body quantum dynamics to much larger times than otherwise possible. We have applied this algorithm to the understanding of typical quantum systems that reach thermal equilibrium at long times, and have also used it to analyse and provide theoretical support to an experimental activities on driven NV centres in diamond.

The second important tool is a way to check if a given system is in a topological state or not. This tool is what is called a local topological marker. Such markers existed before in even dimensions, but we have found a nice way of also writing down markers that work for odd dimensional systems. We have applied this to analyse topological states in amorphous topological matter. We have further extended this to interacting systems.

The third tool we introduced is an effective model for local integrals of motion, which are emergent conserved degrees of freedom in many-body localised systems. Having an effective model of such l-bits allows us to simulate much larger systems to significantly longer times than was possible priorly. We have applied this to understand the entropy induced by fluctuations in the number of particles in a many-body localised system, and have from this gotten deeper insights into comparisons of these emergent models with microscopic models that may, or may not, lead to many-body localisation.

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)

All three of the tools we have introduced lead to progress beyond the state of the art. This can be in the form of allowing us to go to larger systems or longer times, both important for understanding how robust the physics of finite systems is when going to the thermodynamic limit of very large macroscopic systems. Or it was in the form of a tool that can be used to characterise the topological properties of a given quantum state, where before there was a lack of such tools. This has allowed us to address questions that were not possible to really address in the absence of such tools.

These tools are central to the project and going forward towards the end of the project, we plan to develop them further. Especially the LITE algorithm we want to apply to systems showing different types of dynamics, especially those that do now follow the standard expectations of thermodynamics. In many of these cases it is important to be able to go long times to make sure that the deviations from thermodynamic expectations are not just happening at short times, but rather persist also to long times. For this our approach is ideal. The l-bit model that we have applied to the number entropy is a generic and flexible model that can be used to calculate essentially any observable or dynamics in the many-body localised phase. We plan to to this systematically, exploring to what extend slow dynamics or creep in microscopic models can be explained within the phenomenology of many-body localisation, and conversely, more clearly establish which features are not consistent with many-body localisation. Finally, we will continue to explore the physic of amorphous topological insulators and its interplay with localisation physics.