The main scientific and technological achievement is the development of the Tensor Flow Equation (TFE) technique, a novel numerical method for the simulation of complex quantum systems on classical computers. In particular, this numerical method leverages the massively parallel power of graphics processing units (GPUs) to approximately diagonalise (‘solve’) many-body quantum systems in a computationally efficient way, allowing us to compute the non-equilibrium dynamics of large complex systems up to extremely long timescales. This enabled a detailed investigation of quantum memory effects in both one- and two-dimensional quantum systems.
The improvements came in the form of two main breakthroughs, one technological and one conceptual. On a technological level, the method was entirely rewritten to leverage the massively parallel processing capabilities of modern graphics processing units (GPUs) to deliver performance that cut the simulation time by several orders of magnitude over the CPU-based version of the technique. On a conceptual level, the regime of validity of the technique has been hugely enhanced by the development of scrambling transforms, which take a method designed for strongly disordered quantum systems and turn it into a technique which can simulate even entirely homogeneous, non-disordered matter. Secondarily, this development also enhances the speed and efficiency of the technique, delivering vital performance improvements that allow cutting edge high performance computing hardware to be pushed close to its limits.
The main results of the work include the following: the development of the TFE technique and its extension to run on GPUs; the introduction of 'dilute disorder' as a phenomenological bridge between random and homogeneous systems, allowing the systematic investigation of rare-region effects; the detailed numerical investigation of how continuous non-Abelian symmetries can affect localisation and potentially lead to its demise over extremely long timescales; the development of a technique to experimentally reconstruct the building blocks of many-body localisation, an enigmatic phase of matter with many counter-intuitive properties; an investigation into the phenomenology of localisation in disorder-free systems and the finding that these materials exhibit qualitatively different behaviour that may imply slow loss of memory over very long timescales, and finally the finding that quantum memory effects appear to persist in two dimensions to long (but not necessarily infinitely long) times provided the disorder is pseudo-random rather than truly random. These results constitute some early steps towards the challenging process of connecting glassiness with many-body localisation.
