Correlations in incompressible quantum liquid states: constructions of electronic trial wavefunctions

John J. Quinn

Incompressible quantum liquid (IQL) states occur when the single particle angular momentum l and the number N of electrons in the partially filled Landau level satisfy the equation 2l = ν−1N − Cν. ...

Silvia Viola Kusminskiy

Gurinder S. Atwal

Milica V. Milovanović, Th. Jolicœur, Ivana Vidanović

Some fractional quantum Hall states observed in experiments may be described by first-quantized wavefunctions with special clustering properties such as the Moore-Read Pfaffian for filling factor $\ensuremath{\nu}=5/2$. This wavefunction has been constructed by constructing correlation functions of a two-dimensional conformal field theory (CFT) involving a free boson and a Majorana fermion. By considering other CFTs many other clustered states have been proposed as candidate fractional quantum Hall states under appropriate circumstances. It is believed that the underlying CFT should be unitary if one wants to describe an incompressible, i.e., gapped liquid state. We show that by changing the way one derives the wavefunction from its parent CFT it is possible to obtain an incompressible candidate state when starting from a nonunitary parent. The construction mimics a global change in parameters in the phase space of the electron system. We explicit our construction in the case of the so-called Gaffnian state (a state for filling factor 2/5) and also for the Haldane-Rezayi state (a spin-singlet state at filling 1/2). We note that there are obstructions along this path in the case of the permanent spin-singlet state of Read and Rezayi which can be characterized as a robust gapless state.

Steven Allan Kivelson

Electrons in two dimensions in a high magnetic field can condense into an incompressible quantum fluid state when the electron density is equal to certain rational fractions of the flux density. Much progress has been made in understanding the nature of this state based on the ansatz wavefunction of Laughlin. Here, we show that the incompressible nature of the quantum fluid can be derived from a semiclassical evaluation of the imaginary time propagator. The dominant classical paths consist of cooperative ring exchange events. When these condense, they mediate a logarithmic interaction between density fluctuations, and produce a precise fractional quantization condition for the quasi-particle charges. We further show that the essential long wavelength properties of Laughlin's ground state and quasi-particle wavefunctions can be derived constructively from this approach. We conclude with some speculations concerning the nature of the off-diagonal order in the quantum Hall liquid.

Philippe Nozières, David Pines