Open dynamics of interacting and disordered quantum systems

The work in this project concerns the theoretical description of the dynamics of complex quantum systems which are connected to multiple heat baths. There is a particular emphasis on making numerical models where inter-particle interactions and quasi-random or random disorder or impurities are included. We are particularly interested in regimes which are currently not accessible to conventional methodology such as for strong interaction strengths and beyond linear response.

Scientific activity in the area of nanoscale thermodynamics has been boosted over the last years by the importance society is placing on sustainable energy for the worlds population. The current status of steady state like quantum thermo-electics is that they have huge potentiality for making devices more energy efficient but it is not clear what are the fundamental microscopic properties. In addition with the proliferation of quantum technologies it becomes increasingly important to understand the non-equilibrium thermodynamics of such devices.

The overall objective of the project is to understand how the interplay of interactions and imperfection combine to influence non equilibrium thermodynamics and how these effects can possibly be harnessed to provide enhanced thermal functionality. In tackling this core objective many other extremely fundamental topics are analysed which includes heat transport in non ergodic quantum manybody systems.

The work performed in the period covered by the report was in five main areas.
1. The development of a tensor network code to perform boundary driving in non-ergodic spin chain models.
2. The development of mesoscopic leads approach to extend this to finite temperatures.
3. The analysis of the thermodynamics of precision for quantum systems and the physics of quantum non equilibrium steady states.
4. Studies of the off diagonal matrix elements in the eigenstate thermalisation hypothesis.
5. Studies of the non equilibrium thermodynamics of quasi-periodic systems with a single particle mobility edge

The development of a technique which can access the non equilibrium steady state thermodynamics of non quadratic systems is a significant advance in numerical methodology. The current state of the art is either restricted to high temperatures (boundary driving) or restricted to a perturbative regime (NEGF). The technique goes beyond weak coupling and weak interactions

My group is currently working to further improve this and in particular allow for extension to time-dependent Hamiltonians to explore new precision bounds with a wider regime of applicability. I hope to apply this technique to very recent experiments in a quantum electromechanics (lead by Prof. Natalia Ares) at the University of Oxford. We working on a technique to extract equilibrium and non-equilibrium information from non-ergodic quantum systems and in particular how kernel polynomial methods can be combined with MPS/MPO techniques to extract micro-canonical correlation functions. This should supplement our open system calculations. A long term goal would be to develop methods to explore NESS thermodynamics in higher dimensional systems but it is unlikely to be possible within the timeframe of the project.

In the course of the project we have also made fundemtnal contributions to the theory of thermodynamics of precision in quantum systems, using quasi periodic geometry as a tool for quantum thermal technology and also have made contributions to the analysis of the off diagonal eigenstate thermalisation hypothesis.

Periodic Reporting for period 3 - ODYSSEY (Open dynamics of interacting and disordered quantum systems)

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