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Open Many-body Non-Equilibrium Systems

Periodic Reporting for period 3 - OMNES (Open Many-body Non-Equilibrium Systems)

Reporting period: 2019-10-01 to 2021-03-31

With OMNES we are striving to deepen our understanding of non-equilibrium dynamics of systems of many interacting particles, both in classical and quantum dynamics, mainly through exact and rigorous analysis of exactly solvable models. We focus on lattice systems in low (one or two) spatial dimensions and having local (say, nearest neighbour) interactions. Exactly solvable paradigmatic models which are representatives of their universality classes are of crucial importance in theoretical physics since they give us the basic understanding of complex collective phenomena. Within OMNES we are deriving such models for dynamics and statistical mechanics far from thermal equilibrium. For reaching that goals we have to as well develop new mathematical methods, which as equally important objective of OMNES. Both aspects, namely that of obtaining new exactly solved models and developing new mathematical methods for non-equilibrium dynamics, are of fundamental importance for expanding human knowledge and could have potential future applications in developing nanoscale devices that manipulate quantum or classical information.
Within implementation of the project in the first period, we have already achieved several of the important goals that have been set in the proposal, which are elaborated in more detail in the Scientific report.
Specifically, we list below the most important achievements:

- We have developed a general proof of quantum chaos conjecture for interacting quantum spin 1/2 chains with long-range interactions, which is in some sense analogous to periodic orbit theory in semi-classical systems. The idea has been implemented within the family of kicked Ising chains and shown to yield numerically accurate results

- We have presented a rigorous proof of quantum chaos conjecture for a family of spin 1/2 chains with local interactions, specifically for self-dual kicked Ising chains

- We have derived a general inequality for high-temperature diffusion constant in quantum lattice systems in terms of curvature of Drude weights with respect to filling/magnetization/chemical potential parameter

- We have found and solved an exactly solvable deterministic (nonrandom) model for diffusion

- We have found several exactly solable properties of interacting reversible classical cellular automata, specifically the Rule 54
All the points listed above go substantially beyond the state of the art. We plan to work along the lines set in the proposal and this report also in the second period of the project. The main challenge that remains is to obtain some rigorous result on weak integrability breaking (Pillar II), perhaps in the context of many-body localization. Another aspect that we wish still to achieve fundamental breakthrough is in studying exact non-equilibrium dynamics in models with two spatial dimensions.
Fractal Spin Drude weight for Integrable 6-vertex quantum circuit