Hubbard interaction at finite $T$ on a hexagonal lattice

Lado Razmadze; Thomas Luu

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arXiv · 2411.03196

Hubbard interaction at finite $T$ on a hexagonal lattice

Lado Razmadze·Thomas Luu

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Abstract

The temporal finite volume induces significant effects in Monte Carlo simulations of systems in low dimensions, such as graphene, a 2-D hexagonal system known for its unique electronic properties and numerous potential applications. In this work, we explore the behavior of fermions on a hexagonal sheet with a Hubbard-type interaction characterized by coupling $U$. This system exhibits zero or near zero-energy excitations that are highly sensitive to finite temperature effects. We compute corrections to the self-energy and the effective mass of low-energy excitations, arriving at a quantization condition that includes the temporal finite volume. These analyses are then conducted for both zero and finite temperatures. Our findings reveal that the first-order $\mathcal{O}(U)$ contributions are absent, leading to non-trivial corrections starting at $\mathcal{O}(U^2)$. We validate our calculations against exact and numerical results obtained from Hybrid Monte Carlo simulations on small lattices.

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Lado Razmadze, Thomas Luu. 2024-11-05. Hubbard interaction at finite $T$ on a hexagonal lattice. https://arxiv.org/abs/2411.03196

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