Bulletin of the American Physical Society
APS March Meeting 2015
Volume 60, Number 1
Monday–Friday, March 2–6, 2015; San Antonio, Texas
Session Y52: Invited Session: Geometrical Properties of Quantum Hall Fluids |
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Sponsoring Units: DCMP Chair: Eduardo Fradkin, University of Illinois at Urbana-Champaign Room: Grand Ballroom C2 |
Friday, March 6, 2015 8:00AM - 8:36AM |
Y52.00001: Geometry of Fractional Quantum Hall Fluids Invited Speaker: Gil Young Cho Fractional quantum Hall (FQH) fluids of two-dimensional electron gases (2DEG) in large magnetic fields are fascinating topological states of matter. As such they are characterized by universal properties such as their fractional quantum Hall conductivity, fractionally charged anyonic excitations and a degeneracy of topological origin on surfaces with the topology of a torus. Quite surprisingly these topological fluids also couple to the geometry on which the 2DEG resides and have universal responses to adiabatic changes in the geometry. These responses are given by a Wen-Zee term (which describes the coupling of the currents to the spin connection of the geometry) and a gravitational Chern-Simons term which reflects the universal energy and momentum transport along the edges of the FQH state. We use a field theory of the FQH states to derive these universal responses [1,2]. To account for the coupling to the background geometry, we show that the concept of flux attachment needs to be modified and use it to derive the geometric responses from Chern-Simons theories. We show that the resulting composite particles minimally couple to the spin connection of the geometry[1]. Taking account of the framing anomaly of the quantum Chern-Simons theories[2], we derive a consistent theory of geometric responses from the Chern-Simons effective field theories and from parton constructions, and apply it to both abelian and non-abelian states.\\[4pt] [1] Cho, You, and Fradkin, Phys. Rev. B 90, 115139 (2014)\\[0pt] [2] Gromov, Cho, You, Abanov, and Fradkin, arxiv:1410.6812 (2014) [Preview Abstract] |
Friday, March 6, 2015 8:36AM - 9:12AM |
Y52.00002: Theory of the quantum Hall nematic transition Invited Speaker: Joseph Maciejko The discovery of novel types of macroscopic order in quantum many-particle systems is an important goal of condensed matter physics. The fractional quantum Hall (FQH) nematic is a conjectured state of matter in which a fractional quantized Hall conductivity indicative of topological order coexists with the spontaneous breaking of rotational symmetry characteristic of a nematic liquid crystal. Recent experiments suggest that this state may form in 2D electron gases in the first Landau level. In this talk I will present a theory of the quantum phase transition between an isotropic FQH liquid and a FQH nematic state. [Preview Abstract] |
Friday, March 6, 2015 9:12AM - 9:48AM |
Y52.00003: Hall viscosity Invited Speaker: Nicholas Read Viscosity is a transport coefficient relating to transport of momentum, and usually thought of as the analog of friction that occurs in fluids and solids. More formally, it is the response of the stress to the gradients of the fluid velocity field, or to the rate of change of strain (derivatives of displacement from a reference state). In general, viscosity is described by a fourth-rank tensor. Invoking rotation invariance, it reduces to familiar shear and bulk viscosity parts, which describe dissipation, but it can also contain an antisymmetric part, analogous to the Hall conductivity part of the conductivity tensor. In two dimensions this part is a single number, the Hall viscosity. Symmetry of the system under time reversal (or, in two dimensions, reflections) forces it to vanish. In quantum fluids with a gap in the bulk energy spectrum and which lack both time reversal and reflection symmetries the Hall viscosity can be nonzero even at zero temperature. For integer quantum Hall states, it was first calculated by Avron, Seiler, and Zograf, using a Berry curvature approach, analogous to the Chern number for Hall conductivity. In 2008 this was extended by the present author to fractional quantum Hall states and to BCS states in two dimensions. I found that the general result is given by a simple formula $ns/2$, where $n$ is the particle number density, and $s$ is the ``orbital spin'' per particle. The spin $s$ is also related to the shift $S$, which enters the relation between particle number and magnetic flux needed to put the ground state on a surface of non-trivial topology with introducing defect excitations, by $S=2s$; the connection was made by Wen and Zee. The values of $s$ and $S$ are rational numbers, and are robust---unchanged under perturbations that do not cause the bulk energy gap to collapse---provided rotation as well as translation symmetry are maintained. Hall viscosity can be measured in principle, though a simple way to do so is lacking. It enters various theoretical calculations of other properties, and can be used as a diagnostic tool to distinguish phases. The talk will review these results, describing different microscopic approaches to calculating Hall viscosity, robustness, and the relation with effective field theories. [Preview Abstract] |
Friday, March 6, 2015 9:48AM - 10:24AM |
Y52.00004: Spacetime symmetries, Newton-Cartan geometry and the quantum Hall effect Invited Speaker: Dam Son Spacetime symmetries place powerful constraints on the physics of quantum Hall states from spacetime symmetries. These symmetries can be seen by putting the quantum Hall system on a curved manifold. By doing so, one discovers that the action is invariant with respect to time-preserving diffeomorphisms. The diffeomorphism invariance remains nontrivial on the lowest Landau level when inter Landau level mixing is negligible. In the talk we will extract physical consequences of the diffeomorphism invariance for physical observables in flat space. In particular, we relate the leading dependence of the Hall conductivity on wavenumber to the shift. We show how the spectral densities of the components of the stress tensor satisfy several sum rules, one of which involves the static projected structure factor and another involves the shift. From the sum rules one can deduce an inequality between the leading $k^4$ coefficient of the static structure factor and the shift. The inequality is saturated for a large class of trial wavefunctions. The sum rules suggest that if the magneto-roton continues to exist as a sharp resonance at small wavenumber, it should be a ``chiral massive graviton,'' i.e., a particle with spin 2 of one circular polarization. This is demonstrated explicitly in a toy model, where which the sum rules are saturated by one single gapped mode. We argue that the circular polarization of the magneto-roton can be in principle observed by polarized Raman scatterings. The most convenient formalism to write down effective actions satisfying local diffeomorphism invariance turns out to be the Newton-Cartan formalism, introduced by Elie Cartan in 1922-1923 in his attempt to rewrite Newton's gravity in a coordinate-invariant way. We describe the structure of the Newton-Cartan space, including the construction of the connection. [Preview Abstract] |
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