Calculating properties of the Fermi-Hubbard model using advanced numerical techniques

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Summary: The project I am working on aims to calculate various properties of the Fermi-Hubbard model using the most up to date numerical techniques available. The Diagrammatic based algorithm that we are using is the best available for a certain range of parameters of the model and this is a particularly important range of parameters since it is the range that current quantum simulation experiments using ultracold gases are reaching.The technique for evaluating the involves using data calculated from the diagrammatic monte carlo numerical calculations to find the power series expansion of a relevant observable in some parameter. What I will be doing is developing ways to use this information to calculate qunatities of interest, either directly from the series or using more complex techniques to find more information indirectly. The novel content of the project is the furthering of the capabilities of the field to accurately calculate properties of many electron systems with controlled errorbars. The project may end up attempting to extend or improve upon the algortihm to calculate the series coefficients to higher orders or for more exotic quantites and/or calculating experimentally or numerically interesting quantities using the algorithm in its current form.