Dynamics of the edge of a topological quantum fluid with and without emergent conformal symmetry

• Main Author: Tan, Fei
• Other Authors: Yang Bo
• Format: Final Year Project
• Language: English
• Published: Nanyang Technological University 2024
• Subjects: Physics; Condensed matter physics; Fractional quantum Hall effect; Thermal Hall effect
• Online Access: https://hdl.handle.net/10356/175689
• Institution: Nanyang Technological University

The fractional quantum Hall (FQH) effect has become one of the most studied phenomena in condensed matter physics for the past 40 years. One classic approach studying these systems is to compute their thermal Hall conductance (THC) since it can be a quantized quantity for certain FQH states and they do not depend on the details of the system. The quantized value of THC, which is an integer or fractional value in units of $\kappa_0$ ($\kappa_0 = \pi^2 k_B^2/(3h)$), can be used to determine the non-Abelian nature of FQH states. This quantization however can only be robust if the edge of the system is modelled by using the chiral Luttinger liquid ($\chi$LL) under the linear dispersion. In experiments, this model may break down due to the nonlinearity of the confinement potential and the finite temperature effect. In this thesis, we focus on the deviation of the measurable THC of FQH states from the quantized values in the ideal conditions. Instead of heavily relying on the effective conformal field theory (CFT), we derived the THC of both Abelian and non-Abelian states (the wavefunctions of which are Jack polynomials) by using the idea of bulk-edge correspondence, and thus the microscopic counting of the quasihole states. The THC corrections of the FQH edge modes with (i) finite-size/low-temperature corrections, (ii) a more general dispersion relation has been analytically discussed in details. Further numerical results confirmed the behaviors of the THC under these conditions, and we make a conjecture that the THC can only be the universal quantity under linear dispersion. The techniques we use can be easily generalized to other systems with quantized THC, such as other FQH states and the spin liquid. The non-universal corrections can provide guidance for a reasonable error range of THC measurements in experiments and distinguish the different asymptotic behaviors of the candidate states at the same filling.