arXiv subjects

T. Can

Publications and source records attributed to T. Can.

7 recordsLinked to original sources

arXiv2017

Quantum Hall States and Conformal Field Theory on a Singular Surface

In [Can et al. 2016], quantum Hall states on singular surfaces were shown to possess an emergent conformal symmetry. In this paper, we develop this idea further and flesh out details on the emergent conformal symmetry in holomorphic adiabatic states, which we define in the paper. We highlight the connection between the universal features of geometric transport of quantum Hall states and holomorphic dimension of primary fields in conformal field theory. In parallel we compute the universal finite-size corrections to the free energy of a critical system on a hyperbolic sphere with conical and cusp singularities, thus extending the result of Cardy and Peschel for critical systems on a flat cone [Cardy, Peschel 1988], and the known results for critical systems on polyhedra and flat branched Riemann surfaces.

hep-th↗

arXiv2016

Emergent Conformal Symmetry of Quantum Hall States on Singular surfaces

We show that quantum Hall states on surfaces with conical singularities behave as conformal primaries near the singular points, with a conformal dimension controlled by the gravitational anomaly. We show that the electronic fluid at the cone tip possesses an intrinsic angular momentum equal to the conformal dimension, in units of the Planck constant. Finally, we argue that the gravitational anomaly also controls { the fine structure of electronic density at the tip, and } the exchange statistics of cones in the Laughlin states, arising from adiabatically braiding conical singularities. Thus, the gravitational anomaly, which appears as a finite size correction on smooth surfaces, dominates geometric transport on singular surfaces.

cond-mat.str-el↗

arXiv2014

Collective Field Theory for Quantum Hall States

We develop a collective field theory for fractional quantum Hall (FQH) states. We show that in the leading approximation for a large number of particles, the properties of Laughlin states are captured by a Gaussian free field theory with a (filling fraction dependent) background charge. Gradient corrections to the Gaussian field theory arise from ultraviolet regularization. They are the origin of the gravitational anomaly and are described by the Liouville theory of quantum gravity. The field theory simplifies the computation of correlation functions in FQH states and makes manifest the effect of quantum anomalies.

cond-mat.str-el↗

arXiv2014

Geometry of Quantum Hall States: Gravitational Anomaly and Kinetic Coefficients

We show that universal transport coefficients of the fractional quantum Hall effect (FQHE) can be understood as a response to variations of spatial geometry. Some transport properties are essentially governed by the gravitational anomaly. We develop a general method to compute correlation functions of FQH states in a curved space, where local transformation properties of these states are examined through local geometric variations. We introduce the notion of a generating functional and relate it to geometric invariant functionals recently studied in geometry. We develop two complementary methods to study the geometry of the FQHE. One method is based on iterating a Ward identity, while the other is based on a field theoretical formulation of the FQHE through a path integral formalism.

cond-mat.str-el↗

arXiv2014

Fractional Quantum Hall Effect in a Curved Space: Gravitational Anomaly and Electromagnetic Response

We develop a general method to compute correlation functions of fractional quantum Hall (FQH) states on a curved space. In a curved space, local transformation properties of FQH states are examined through local geometric variations, which are essentially governed by the gravitational anomaly. Furthermore, we show that the electromagnetic response of FQH states is related to the gravitational response (a response to curvature). Thus, the gravitational anomaly is also seen in the structure factor and the Hall conductance in flat space. The method is based on iteration of a Ward identity obtained for FQH states.

cond-mat.str-el↗

arXiv2014

Singular Behavior At The Edge of Laughlin States

A distinguishing feature of fractional quantum Hall (FQH) states is a singular behavior of equilibrium densities at boundaries. In contrast to states at integer filling fraction, such quantum liquids posses an additional dipole moment localized near edges. It enters observable quantities such as universal dispersion of edge states and Lorentz shear stress. For a Laughlin state, this behavior is seen as a peak, or overshoot, in the single particle density near the edge, reflecting a general tendency of electrons in FQH states to cluster near edges. We compute the singular edge behavior of the one particle density by a perturbative expansion carried out around a completely filled Landau level. This correction is shown to fully capture the dipole moment and the major features of the overshoot observed numerically. Furthermore, it exhibits the Stokes phenomenon with the Stokes line at the boundary of the droplet, decaying like a Gaussian inside and outside the liquid with different decay lengths. In the limit of vanishing magnetic length the shape the overshoot is a singular double layer with a capacity that is a universal function of the filling fraction. Finally, we derive the edge dipole moment of Pfaffian FQH states. The result suggests an explicit connection between the magnitude of the dipole moment and the bulk odd viscosity.

cond-mat.str-el↗

arXiv2013

Exact and asymptotic features of the edge density profile for the one component plasma in two dimensions

There is a well known analogy between the Laughlin trial wave function for the fractional quantum Hall effect, and the Boltzmann factor for the two-dimensional one-component plasma. The latter requires analytic continuation beyond the finite geometry used in its derivation. We consider both disk and cylinder geometry, and focus attention on the exact and asymptotic features of the edge density. At the special coupling \Gamma := q^2/k_BT=2 the system is exactly solvable. In particular the k-point correlation can be written as a k \times k determinant, allowing the edge density to be computed to first order in \Gamma - 2. A double layer structure is found, which in turn implies an overshoot of the density as the edge of the leading support is approached from inside the plasma. Asymptotic analysis shows that the deviation from the leading order (step function) value is different for into the plasma than for outside. For general \Gamma, a Gaussian fluctuation formula is used to study the large deviation form of the density for N large but finite. This asymptotic form involves thermodynamic quantities which we independently study, and moreover an appropriate scaling gives the asymptotic decay of the limiting edge density outside of the plasma.

cond-mat.stat-mech↗