TL;DR
This paper investigates how Dirac fermionic fields and effective space-time metrics emerge in low-energy limits of non-relativistic models on graphs, focusing on conditions for Fermi points in various dimensions.
Contribution
It provides a detailed analysis of the emergence of Dirac fermions and space-time metrics from graph-based models, highlighting conditions for Fermi point formation in different dimensions.
Findings
Dirac fermions emerge as effective fields near Fermi points.
Conditions for Fermi point appearance depend on graph structure and dimensionality.
Effective space-time metrics can also arise in the low-energy limit.
Abstract
We study the emergence of Dirac fermionic field in the low energy description of non-relativistic dynamical models on graphs admitting continuum limit. The Dirac fermionic field appears as the effective field describing the excitations above point-like Fermi surface. Together with the Dirac fermionic field an effective space-time metric is also emerging. We analyze the conditions for such Fermi points to appear in general, paying special attention to the cases of two and three spacial dimensions.
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