2024/11/05 by Lado Razmadze, Razmadze, Lado, Thomas Luu +1 · 1 citation
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Strongly Correlated Electrons (cond-mat.str-el)
paper · pdf · doi:10.48550/arxiv.2411.03196
openalex publication_date 2024/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 O(U) contributions are absent, leading to non-trivial corrections starting at O(U2). We validate our calculations against exact and numerical results obtained from Hybrid Monte Carlo simulations on small lattices.