1National Institute for Theoretical Physics (NITheP), Stellenbosch 7600, South Africa
2Institute of Theoretical Physics, Department of Physics, University of Stellenbosch, Stellenbosch 7600, South Africa
3African Institute for Mathematical Sciences, Muizenberg, Cape Town, South Africa
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Abstract
We introduce structured random matrix ensembles, constructed to model many-body quantum systems with local interactions. These ensembles are employed to study equilibration of isolated many-body quantum systems, showing that rather complex matrix structures, well beyond Wigner’s full or banded random matrices, are required to faithfully model equilibration times. Viewing the random matrices as connectivities of graphs, we analyse the resulting network of classical oscillators in Hilbert space with tools from network theory. One of these tools, called the maximum flow value, is found to be an excellent proxy for equilibration times. Since maximum flow values are less expensive to compute, they give access to approximate equilibration times for system sizes beyond those accessible by exact diagonalisation.
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Cited by
[1] Charlie Nation and Diego Porras, “Taking snapshots of a quantum thermalization process: emergent classicality in quantum jump trajectories”, arXiv:2003.08425.
[2] Shoki Sugimoto, Ryusuke Hamazaki, and Masahito Ueda, “Test of Eigenstate Thermalization Hypothesis Based on Local Random Matrix Theory”, arXiv:2005.06379.
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