On the glassy nature of quantum disordered systems – GLADYS

Disorder is often present in condensed matter, in the form of impurities in solids, or in the random arrangement of glasses. It can have dramatic consequences, such as preventing transport or inducing extremely slow relaxation to equilibrium. In the quantum regime, the interplay between interference effects and disorder gives rise to quantum localization, a key mechanism of non-ergodicity in disordered quantum systems. Its most remarkable effects are the insulating nature of disordered materials or the absence of thermalization in closed quantum many-body systems. Spin glass physics is another paradigm of non-ergodic behavior which arises in classical disordered systems. Its study has led to important theoretical breakthroughs like the concept of spontaneous replica symmetry breaking and has found applications in e.g. optimization or biology. The objective of this project is to make a bridge between these two domains of quantum disordered systems and classical glasses. Apart from few notable examples, they have not exchanged many ideas.

This project aims at showing that two paradigmatic quantum disordered problems, Anderson localization and the 1D superfluid-Bose glass transition, have universal glassy properties. Recently, I have shown [G. Lemarié, PRL 122, 030401 (2019)] using extensive numerical simulations that Anderson localization in two dimension at zero temperature shares three important characteristic properties of spin glasses: pinning, avalanches and chaos. Anderson localization confines electron transport along paths which are frozen (pinning) into configurations that sometimes jump brutally into a very different configuration (avalanche). Spin glass chaos characterizes the extreme fragility of these glassy configurations. These glassy properties were found to depend crucially on quantum interferences. This opens a new playground for the study of quantum glassy physics. It will be particularly interesting to see whether these new quantum glassy properties extend to the case of other dimensionalities, in particular in dimension three where the Anderson metal-insulator transition arises, to the case of out-of-equilibrium transport and to the case of high-dimensionalities where the Anderson transition is not well understood. Surprisingly, the glassy properties of the insulating phase of disordered interacting bosons have been little studied. This project aims at explaining why we call this phase a ``Bose glass'' and clarifying the nature of the 1D superfluid-Bose glass transition in the intriguing strong disorder regime.

The approach that I want to follow crucially relies on state of the art numerical simulations. Anderson localization and the 1D superfluid-Bose glass transition are ideal cases to start with because they can be simulated accurately with large system sizes, long times. This will be complemented by scaling theory, and analytical calculations. An interesting perspective of this project is to motivate experiments to consider glassy effects in quantum disordered systems. Anderson localization is a universal phenomenon which arises in many different types of systems, from classical waves to quantum matter waves. The superfluid-insulator transition is experimentally relevant for strongly disordered superconductors, disordered spin chains, Josephson junction arrays and ultracold atoms. In the field of cold atoms, a high degree of control was achieved while experiments in condensed matter systems have local probe techniques to address the non-ergodic properties induced by disorder.

This young researcher project will allow me to develop an original research positioning at the interface between two broad and important communities. The requested scientific budget will fund one postdoc for two years, equipments for numerical simulations, travel expenses for attending conferences and the organization of a conference in Toulouse on this subject.