Critical Theory of Two-Dimensional Mott Transition: Integrability and Hilbert Space Mapping

We reconsider the Mott transition in the context of a two-dimensional fermion model with density-density coupling. We exhibit a Hilbert space mapping between the original model and the Double Lattice Chern-Simons theory at the critical point by use of the representation theory of the q-oscillator and Weyl algebras. The transition is further characterized by the ground state modification. The explicit mapping provides a new tool to further probe and test the detailed physical properties of the fermionic lattice model considered here and to enhance our understanding of the Mott transition(s)

Defining \u27Good\u27: Exploring The Meaning of Politics And Its Relation To The Personal

The US is currently experiencing a confusing and problematic shift in politics under Donald Trump, who continues to disrupt the status quo of American democracy. Such a reality begs us to ask the question of what politics means, and what it should mean for the future. Throughout history, many philosophers and theorists, such as Thomas Hobbes and Max Weber, have identified the meaning of politics as obedience and domination over others. However, such an interpretation is incredibly dangerous, closely aligning with the historical values of authoritarian and totalitarian governments. Political theorist Hannah Arendt provides a solution to this dilemma, exposing the much more productive explanation that politics can only be achieved through the realization of equality. Additionally, she demonstrates that the key to this political utopia lies within the personal, as her humanistic concept of ‘plurality’ sheds light on how true politics can be achieved within society. Further, through such recognition, we can illuminate the dangers that the world faces when authority figures do not possess such a quality

The W1+∞W_{1 + \infty } effective theory of the Calogero- Sutherland model and Luttinger systems.

We construct the effective field theory of the Calogero-Sutherland model in the thermodynamic limit of large number of particles $N$. It is given by a \winf conformal field theory (with central charge $c=1$) that describes {\it exactly} the spatial density fluctuations arising from the low-energy excitations about the Fermi surface. Our approach does not rely on the integrable character of the model, and indicates how to extend previous results to any order in powers of $1/N$. Moreover, the same effective theory can also be used to describe an entire universality class of $(1+1)$-dimensional fermionic systems beyond the Calogero-Sutherland model, that we identify with the class of {\it chiral Luttinger systems}. We also explain how a systematic bosonization procedure can be performed using the \winf generators, and propose this algebraic approach to {\it classify} low-dimensional non-relativistic fermionic systems, given that all representations of \winf are known. This approach has the appeal of being mathematically complete and physically intuitive, encoding the picture suggested by Luttinger's theorem.Comment: 13 pages, plain LaTeX, no figures

Coulomb Blockade in Hierarchical Quantum Hall Droplets

The degeneracy of energy levels in a quantum dot of Hall fluid, leading to conductance peaks, can be readily derived from the partition functions of conformal field theory. Their complete expressions can be found for Hall states with both Abelian and non-Abelian statistics, upon adapting known results for the annulus geometry. We analyze the Abelian states with hierarchical filling fractions, \nu=m/(mp \pm 1), and find a non trivial pattern of conductance peaks. In particular, each one of them occurs with a characteristic multiplicity, that is due to the extended symmetry of the m-folded edge. Experimental tests of the multiplicity can shed more light on the dynamics of this composite edge.Comment: 8 pages; v2: published version; effects of level multiplicities not well understood, see arXiv:0909.3588 for the correct analysi

Algebraic bosonization: the study of the Heisenberg and Calogero-Sutherland models

We propose an approach to treat (1+1)--dimensional fermionic systems based on the idea of algebraic bosonization. This amounts to decompose the elementary low-lying excitations around the Fermi surface in terms of basic building blocks which carry a representation of the W_{1+\infty} \times {\overline W_{1+\infty}} algebra, which is the dynamical symmetry of the Fermi quantum incompressible fluid. This symmetry simply expresses the local particle-number current conservation at the Fermi surface. The general approach is illustrated in detail in two examples: the Heisenberg and Calogero-Sutherland models, which allow for a comparison with the exact Bethe Ansatz solution.Comment: 51 pages, plain LaTe

ANALYSIS OF URBAN SURFACE BIOPHYSICAL DESCRIPTORS AND LAND SURFCACE TEMPERATURE VARIATIONS IN JIMETA CITY, NIGERIA

oai:ojs2.socialscienceresearch.org:article/10000

The extended conformal theory of the Calogero-Sutherland model

We describe the recently introduced method of Algebraic Bosonization of (1+1)-dimensional fermionic systems by discussing the specific case of the Calogero-Sutherland model. A comparison with the Bethe Ansatz results is also presented.Comment: 12 pages, plain LaTeX, no figures; To appear in the proceedings of the IV Meeting "Common Trends in Condensed Matter and High Energy Physics", Chia Laguna, Cagliari, Italy, 3-10 Sep. 199