Small Fermi Surfaces and Strong Correlation Effects in Dirac Materials with Holography

Recent discovery of transport anomaly in graphene demonstrated that a system known to be weakly interacting may become strongly correlated if system parameter(s) can be tuned such that fermi surface is sufficiently small. We study the strong correlation effects in the transport coefficients of Dirac materials doped with magnetic impurity under the magnetic field using holographic method. The experimental data of magneto-conductivity are well fit by our theory, however, not much data are available for other transports of Dirac material in such regime. Therefore, our results on heat transport,thermo-electric power and Nernst coefficients are left as predictions of holographic theory for generic Dirac materials in the vicinity of charge neutral point with possible surface gap. We give detailed look over each magneto-transport observable and 3Dplots to guide future experiments.Comment: 32 pages, 24 figure

Mott transition with Holographic Spectral function

We show that the Mott transition can be realized in a holographic model of a fermion with bulk mass, $m$, and a dipole interaction of coupling strength $p$. The phase diagram contains gapless, pseudo-gap and gapped phases and the first one can be further divided into four sub-classes. We compare the spectral densities of our holographic model with the Dynamical Mean Field Theory (DMFT) results for Hubbard model as well as the experimental data of Vanadium Oxide materials. Interestingly, single-site and cluster DMFT results of Hubbard model share some similarities with the holographic model of different parameters, although the spectral functions are quite different due to the asymmetry in the holography part. The theory can fit the X-ray absorption spectrum (XAS) data quite well, but once the theory parameters are fixed with the former it can fit the photoelectric emission spectrum (PES) data only if we symmetrize the spectral function.Comment: 22 pages, 21 figures, v2 symmetrization arguments are abandoned, the argument of Mott transition is still valid, but comparison with Hubbard model is modified. Title is change

Bounds on ρ\rho-invariants and simplicial complexity of triangulated manifolds

We show the existence of linear bounds on Atiyah-Singer $\rho$-invariants of PL manifolds, employing a new combinatorial concept of $G$-colored polyhedra. As application, we show that how the number of h-cobordism classes of manifolds simple homotopy equivalent to a lens space with $V$ simplices and the fundamental group of $\mathbb{Z}_n$ grows in $V$. Furthermore we count the number of homotopy lens spaces with bounded geometry in $V$. Similarly, we give new linear bounds on Cheeger-Gromov $\rho$-invariants of PL manifolds endowed with a faithful representation also. A key idea is to construct a cobordism with a linear complexity whose boundary is $\pi_1$-injectively embedded, using relative hyperbolization. As application, we study the complexity theory of high-dimensional lens spaces. Lastly we show the density of $\rho$-invariants over manifolds homotopy equivalent to a given manifold for certain fundamental groups. This implies that the structure set is not finitely generated.Comment: 19 pages, 7 figure

The Trinitarian Ontology of Jonathan Edwards: Glory, Beauty, Love, and Happiness in the Dispositional Space of Creation

This dissertation explores Jonathan Edwards’ trinitarian logic and ontology of God’s glory which integrate the innovative facets of his thoughts that previous studies have only partially articulated. Edwards’ trinitarian framework overarching his doctrines of God, creation, and being provides an alternative ontological foundation which validates the actual reality of Christian faith and experience and reconstructs Christian theology and life. Edwards’ trinitarian logic dialectically integrates the opposing poles of God’s perfection in being and in personhood, God’s creation out of nothing and through emanation, and God’s transcendence and immanence. Preliminarily, chapter two examines how in Edwards’ theocentric thought the Christian experience of divine revelation and salvation constitutes the two poles of God’s perfection in being and personhood. Chapters three through five elaborate Edwards’ synthesis of the polarity of God’s existence. By virtue of the biblical idea of God’s glory, Edwards defines the perfection of God’s existence as the spiritual space of the Trinity, that is, the dispositional ground of being to communicate the divine self. The trinitarian being of God incorporates the christological, soteriological, and pneumatological structure of God’s trinitarian presence in relation to the world. The trinitarian being of God determines the divine act of creation out of nothing as the communication of divine ideas by the Son through the emanation of the Spirit. By way of conclusion, chapter seven demonstrates that Edwards’ trinitarian structure of God’s being and act constructs a trinitarian immaterialism of dispositional ontology that integrates the semiotic, aesthetic, affectional, rhetorical, axiological, and ethical aspects of being; chapter eight argues that the trinitarian ontology proposes a soteriological, trinitarian, and asymmetrically perichoretic panentheism of non-dualistic personal theism. Edwards’ trinitarian dialectics specifies the perfection of being as the glorious beauty of happy life in the communion of love that constitutes the relation of asymmetrical union with distinction. The trinitarian logic and ontology propose a worldview of the regenerated that is derived from the singular Christian experience of God’s salvation and revelation through Jesus Christ and his Spirit and integrates the Christian faith with life in the world by framing harmonious relations between God, humanity, and nature