A Caltech Library Service

New Tensor Network Methods and Studies of Criticality in Low-Dimensional Quantum Systems


Roberts, Brenden Carlisle (2021) New Tensor Network Methods and Studies of Criticality in Low-Dimensional Quantum Systems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/vhwq-gz88.


Several investigations are presented around the general topic of the ground state and low-energy behavior of models for many-body quantum physics in one dimension (1d). We develop a novel numerical method for the ground and low-energy sectors of local Hamiltonians in 1d which is based on proofs from quantum information theory. This method, the rigorous renormalization group (RRG), enjoys the benefits of explicit global information from the Hamiltonian in its local step, allowing it to avoid spurious convergence in systems with challenging energy landscapes. We apply RRG to the random XYZ spin chain in an unbiased numerical study evaluating infinite-randomness fixed point physics and continuously varying critical exponents in the ground state, finding evidence for both. In a related effective model with correlations preventing the exact solution of the strong-disorder renormalization group equations, we use the framework of random walks to rigorously establish continuously varying critical exponents. We also perform detailed studies of deconfined quantum critical points (DQCP) in 1d, providing strong evidence for phase transitions which display similar phenomenology to the canonical examples in 2d. A family of DQCP phase transitions in 1d is exhibited which appears to controlled by complex fixed points corresponding to a walking scenario for renormalization group flows.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Condensed matter theory; quantum critical points; renormalization group
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Motrunich, Olexei I.
Thesis Committee:
  • Alicea, Jason F. (chair)
  • Refael, Gil
  • Simmons-Duffin, David
  • Motrunich, Olexei I.
Defense Date:25 May 2021
Record Number:CaltechTHESIS:05122021-000037101
Persistent URL:
Related URLs:
URLURL TypeDescription adapted for ch. 2 adapted for ch. 4 adapted for ch. 5
Roberts, Brenden Carlisle0000-0002-3107-1878
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:14145
Deposited By: Brenden Roberts
Deposited On:03 Jun 2021 23:48
Last Modified:28 Oct 2021 18:29

Thesis Files

[img] PDF - Final Version
See Usage Policy.


Repository Staff Only: item control page