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Aspects of critical spin 1 chains and 2 dimensional symmetry protected topological phases of matter
No full textEffective field theory is a very useful technique for understanding quantum many body systems. We use this approach to study a certain class of critical quantum spin-1 chains and symmetry protected topological phases of matter in two spatial dimensions.
In the first context we consider the SU(3) symmetric spin-1 chain with additional interactions. We use bosonization to demonstrate that the effective field theories describing the critical behaviour of these spin chains can be mapped to free compact boson conformal field theories (CFTs) with central charge c=2. We also describe how some predictions from field theory can be verified in numerical calculations using exact diagonalization (ED) and the density matrix renormalization group (DMRG) algorithm. In particular, the bosonization method gives a formula for the evolution of four Tomonaga-Luttinger liquid (TLL) parameters as a function of the lattice parameters. Using the analytic formulae for the scaling dimensions in terms of the TLL parameters and matching of lowest scaling dimensions, we numerically calculate these field-theoretic parameters and confirm that their evolution agrees with the prediction using bosonization.
We also tackle aspects of the challenging problem of understanding interacting topological phases. In this context, we aim to understand the effects if interactions in certain classes of symmetry protected topological (SPT) phases of matter. We consider non-chiral SPT phases in two spatial dimensions protected by a discrete symmetry such as Z_K or Z_K x Z_K symmetry. We argue that modular invariance/noninvariance of the partition function of the one-dimensional edge theory can be used to diagnose whether, by adding a suitable potential, the edge theory can be gapped or not without breaking the symmetry. By taking bosonic phases described by Chern-Simons K-matrix theories and fermionic phases relevant to topological superconductors as examples, we demonstrate explicitly that when modular invariance is achieved, we can construct an interaction potential that is consistent with the symmetry and can completely gap out the edge.
We also briefly discuss preliminary results of a numerical approach for simulating the 3 dimensional Landau Level problem. This includes a brief description of a potential application of variational Monte Carlo to spin-orbit coupled ab initio systems.Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2018-05-01The student, Olabode Sule, accepted the attached license on 2016-02-02 at 18:25.The student, Olabode Sule, submitted this Dissertation for approval on 2016-02-02 at 18:39.This Dissertation was approved for publication on 2016-02-03 at 13:28.DSpace SAF Submission Ingestion Package generated from Vireo submission #9061 on 2016-07-07 at 13:48:12Made available in DSpace on 2016-07-07T20:26:46Z (GMT). No. of bitstreams: 3
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Previous issue date: 2016-02-03Embargo set by: Seth Robbins for item 93068
Lift date: 2018-07-07T20:28:14Z
Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD systemEmbargo set by: Seth Robbins for item 93068
Lift date: 2018-07-07T20:35:34Z
Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD systemU of I Only Restriction Lifted for Item 93068 on 2018-07-08T09:15:23Z
