A Caltech Library Service

Topological Phases of Matter: Classification, Stacking Law, and Relation to Topological Quantum Field Theory


You, Minyoung (2021) Topological Phases of Matter: Classification, Stacking Law, and Relation to Topological Quantum Field Theory. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/4xq7-gh61.


We study aspects of gapped phases of matter, focusing on their classification, including the group law under stacking, and their relation to topological quantum field theories (TQFT). In one spatial dimension, it is well-known that Matrix Product States (MPS) efficiently approximate ground states of gapped systems; by showing that these states arise naturally in 1 + 1-dimensional lattice TQFT, which in turn are closely related to continuum TQFT, we provide a concrete connection between ground states of lattice systems and TQFT in 1 + 1 dimensions. We generalize this to systems with symmetries and fermions, and obtain a classification and group law for the stacking of 1 + 1-dimensional symmetry-protected topological phases. Further, we study the effect of turning on/off interactions for the classification: the phase classification of a given symmetry class of Hamiltonians can be different depending on whether we allow interactions or not, and in low dimensions we provide some concrete formulas relating the phases under the non-interacting classification and those under the interacting classification. Lastly, we study the phases of the 2 + 1-dimensional topological superconductor, and show that for all 16 phases braiding statistics of vortices, which determine the underlying TQFT, can be obtained by stacking layers of the basic p + ip superconductor.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Topological phases, condensed matter physics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Kapustin, Anton N.
Thesis Committee:
  • Chen, Xie (chair)
  • Marcolli, Matilde
  • Motrunich, Olexei I.
  • Kapustin, Anton N.
Defense Date:12 June 2020
Record Number:CaltechTHESIS:08272020-235955490
Persistent URL:
Related URLs:
URLURL TypeDescription adapted for Chapter 4, Sections 1 through 4. adapted for Chapter 4, Sections 5 through 8. adapted for Chapter 4, Sections 8 through 10. adapted for Chapter 5. adapted for Chapter 6.
You, Minyoung0000-0002-8251-953X
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:13859
Deposited By: Minyoung You
Deposited On:10 Sep 2020 19:09
Last Modified:28 Feb 2023 19:13

Thesis Files

PDF - Final Version
See Usage Policy.


Repository Staff Only: item control page