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

Citation

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. https://resolver.caltech.edu/CaltechTHESIS:05122021-000037101

Abstract

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.

Thesis Files