Quantum Critical Phenomena of Relativistic Fermions in 1+1d and 2+1d

Loading...
Thumbnail Image

Date

2022

Journal Title

Journal ISSN

Volume Title

Repository Usage Stats

76
views
37
downloads

Abstract

In this dissertation, we study the phase structures and the quantum critical phenomena of relativistic lattice fermions with $\O(2N_f)$ symmetry in one and two spatial dimensions, motivated by the ability to perform efficient Monte Carlo simulations. Close to a quantum critical point, physics is universal and can be described by continuum quantum field theories. We perform a perturbative analysis of all independent four-fermion interactions allowed by the $\O(2N_f)$ symmetry near the free-fermion fixed point. We then analyze the resulting continuum field theories using various techniques. In one spatial dimension, we use the powerful tools from conformal field theory and non-abelian bosonization to understand the renormalization group flows, the correlation functions, and the spectra. In the case of $N_f=2$, we find that by tuning a Hubbard coupling, our model undergoes a second-order phase transition, which can be described by an $\SU(2)_1$ Wess-Zumino-Witten model perturbed by a marginal coupling. We confirm these results using the meron-cluster algorithm, and locate the critical point precisely using exact diagonalization based on the spectrum of the Wess-Zumino-Witten model. In two spatial dimensions, we analyze the model using $\varepsilon$ expansion, large $N_f$ expansion and effective potential methods. In the case of $N_f=2$, we find a novel critical point where the anti-ferromagnetic order and superconducting-CDW order become simultaneously quantum critical, which seems to have been missed in literature. We compare these predictions with the numerical results obtained using the fermion-bag algorithm by Emilie Huffman.

Department

Description

Provenance

Citation

Citation

Liu, Hanqing (2022). Quantum Critical Phenomena of Relativistic Fermions in 1+1d and 2+1d. Dissertation, Duke University. Retrieved from https://hdl.handle.net/10161/25783.

Collections


Dukes student scholarship is made available to the public using a Creative Commons Attribution / Non-commercial / No derivative (CC-BY-NC-ND) license.