Quantum Hall Physics in Low-Dimensional Strongly Correlated Systems

Hideo Aoki

Dmitry Green

This thesis is a theoretical analysis of sample two- and one-dimensional systems. The two-dimensional examples are the quantum Hall liquid and anomalous paired states. The most widely accepted effective theory of the quantum Hall liquid is based on the so-called Chern Simons Lagrangian, but it is not entirely satisfactory. We obtain the first derivation of an alternative effective theory from microscopic principles. Our formulation allows for a first principles derivation of physical quantities such as the effective mass and compressibility and contains the first analytical observation of the magnetoroton. The formalism developed along the way is also applied to paired states in anomalous supeconductors, a topic of much recent interest. The one-dimenisonal system is the carbon nanotube. Gas uptake in nanotube bundles is currently attracting a wealth of research with both applied and fundamental implications. We propose adsorption of gases on the surface of a single tube, finding strong correlations and symmetries that have not been observed yet. The properties of these states are directly relevant to other one-dimensional structures such as spin ladders and stripes and raise interesting and open questions.

R. Tao, Kazumi Maki

Susanne Viefers

The close theoretical analogy between the physics of rapidly rotating atomic Bose condensates and the quantum Hall effect (i.e. a two-dimensional electron gas in a strong magnetic field) was first pointed out ten years ago. As a consequence of this analogy, a large number of strongly correlated quantum-Hall-type states have been predicted to occur in rotating Bose systems, and suggestions have been made for how to manipulate and observe their fractional quasiparticle excitations. Due to a very rapid development in experimental techniques over the past years, experiments on BEC now appear to be close to reaching the quantum Hall regime. This paper reviews the theoretical and experimental work done to date in exploring quantum Hall physics in cold bosonic gases. Future perspectives are discussed briefly, in particular the idea of exploiting some of these strongly correlated states in the context of topological quantum computing.

Murugan, Jeff

We propose a framework for applying on-shell scattering amplitude methods to emergent relativistic phases of quantum matter. Many strongly correlated systems, from Dirac and Weyl semimetals to topological-insulator surfaces, exhibit low-energy excitations that are effectively massless relativistic spinors. We show that physical observables such as nonlinear optical and Hall responses can be obtained from compact on-shell amplitudes, bypassing the complexity of Feynman diagrams. As a concrete demonstration, we derive the nonlinear Hall conductivity of a Dirac semimetal from a single parity-odd three-photon amplitude, highlighting the analytic and conceptual power of amplitude-based approaches for strongly correlated condensed-matter systems.

Peter Prelovšek, Darko Veberič, M W Long +1 more