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arXiv · 2512.23678

Symbolic recursion method for strongly correlated fermions in two and three dimensions

Igor Ermakov·Oleg Lychkovskiy
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Abstract

We present a symbolic implementation of the recursion method for dynamical correlations and transport in fermionic systems on one-, two-, and three-dimensional lattices. The implementation is applicable in the strongly correlated regime, yields results directly in the thermodynamic limit, and covers all time scales, from short times through the thermalization time to the late-time asymptotics. Focusing on two paradigmatic models -- interacting spinless fermions and the Hubbard model -- we confirm the universal operator growth hypothesis in the fermionic case, compute infinite-temperature current-current autocorrelation functions, and determine the charge diffusion constant and the high-temperature conductivity. The diffusion constant is obtained in both the perturbative and the nonperturbative regime of the interaction strength, and we locate the boundary between them. We compare our approach with the Majorana propagation method, which converges up to intermediate times and agrees with ours where converged. Our results highlight a symbolic computational paradigm in which the most expensive step is performed once, producing reusable symbolic output that yields physical observables for arbitrary model parameters.

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Igor Ermakov, Oleg Lychkovskiy. 2025-12-29. Symbolic recursion method for strongly correlated fermions in two and three dimensions. https://arxiv.org/abs/2512.23678

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