Beyond the Dirac Cone: Unveiling Interactions in Exotic Fermions
![The evolution of power [latex]\eta(E)[/latex] within the density of states [latex]\rho(E) \sim E^{\eta(E)}[/latex] demonstrates a transition from linear Dirac behavior at low energies to type-II semi-Dirac characteristics as energy increases, a phenomenon modulated by interaction strengths of [latex]\alpha = 0.05, 0.10, 0.20[/latex] at the Hartree-Fock level and consistent with the interacting spectrum detailed previously.](https://arxiv.org/html/2601.21098v1/x4.png)
New research explores how long-range interactions reshape the behavior of type-II semi-Dirac fermions, impacting their fundamental properties.
![The evolution of power [latex]\eta(E)[/latex] within the density of states [latex]\rho(E) \sim E^{\eta(E)}[/latex] demonstrates a transition from linear Dirac behavior at low energies to type-II semi-Dirac characteristics as energy increases, a phenomenon modulated by interaction strengths of [latex]\alpha = 0.05, 0.10, 0.20[/latex] at the Hartree-Fock level and consistent with the interacting spectrum detailed previously.](https://arxiv.org/html/2601.21098v1/x4.png)
New research explores how long-range interactions reshape the behavior of type-II semi-Dirac fermions, impacting their fundamental properties.

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![With a gluing solution of type (i) and [latex]A_k = 2k = 2g[/latex], the empirical limit of [latex]\mathcal{B}[/latex] is reached at a point where, despite [latex]J = 0[/latex], the effective magnetic moment [latex]m_H[/latex] remains positive at [latex]V = 0[/latex].](https://arxiv.org/html/2601.20955v1/x2.png)
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![Entanglement’s evolution within the modeled wormhole setup demonstrates that localized operator excitation enhances mutual information [latex]\Delta I_{AB} > 0[/latex] by spreading the right-moving entangled mode-primarily affecting region BB, with some impact on AA-while leaving the left-moving mode unaffected, thereby increasing [latex]S_A[/latex] but not altering [latex]S_{AB}[/latex].](https://arxiv.org/html/2601.21604v1/x9.png)
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![FlowBoost successfully generated point sets that surpass previously known constructions, achieving a discrepancy of 0.073086 for [latex]N=20[/latex] and 0.032772 for [latex]N=60[/latex], and approaching the theoretically proven optimal discrepancy of 0.0604 for [latex]N=20[/latex].](https://arxiv.org/html/2601.18005v1/x35.png)
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![The study elucidates a Hamiltonian constructed from specific term configurations-the first three defining the initial component, while subsequent configurations detail further terms-and demonstrates this framework’s application through Gauss’s law as it relates to eleven-form symmetries, further illustrated by the behavior of a dipole algebra-specifically, how a translation operator acting on [latex]\mathcal{M}^{Z(1)}\_{xy,x}[/latex] transforms it to [latex]\mathcal{M}^{Z(1)}\_{xy,0}[/latex].](https://arxiv.org/html/2601.21625v1/x7.png)
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