Conformal field theory and numerical techniques in the fractional quantum hall effect

Thesis

This thesis presents the development of Conformal Field Theory (CFT) methods to analyse the topological properties of fractional quantum Hall effect (FQHE) wave functions, and numerical techniques to find accurate FQHE trial ground state wave functions.

In Chapter 2, we argue that the real-space entanglement spectra (RSES) of generic chiral FQHE ground states have a scaling property, discussed in previous works, where the RSES is given as the spectrum of an operator that is an integral of local operators along the real-space cut that can be expanded in negative powers of the real-space cut length. This is directly tested for the bosonic Composite Fermion (CF) wave functions on the sphere at filling fraction 2/3.

In Chapter 3, it is shown that all chiral Parton-type FQHE ground and edge state trial wave functions, in the planar geometry, can be expressed as CFT correlation functions. A field-theoretic generalisation of Laughlin’s plasma analogy, known as the generalised screening hypothesis, is then formulated for these states, where the implications for inner products of edge state trial wave functions are discussed. These implications of generalised screening are then numerically tested in two specific cases.

In Chapter 4, a method for the energy minimisation of paired CF trial wave functions is discussed, with the goal of producing accurate ground state trial wave functions for electrons, with Coulomb interactions, at filling fraction 5/2. The resulting energetics are then presented for the optimised paired CF versions of the Pfaffian, anti-Pfaffian and particle-hole (PH) symmetric Pfaffian topological orders and are compared to their zero-parameter trial wave function counterparts. It is found that the effective CF pairing in the Pfaffian and anti-Pfaffian wave functions is well approximated by a weak-pairing BCS-type description, and certain pathologies are found for the PH-Pfaffian wave functions.

Authors: Henderson, GJ

• DOI: 10.5287/ora-xmrm7pd4m
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: conformal field theory; topological phases of matter; fractional quantum hall effect
• Subjects: Condensed matter physics