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Short-Range Entangled Phases of Fermions


Turzillo, Alexander Michael (2019) Short-Range Entangled Phases of Fermions. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/3JR4-8G12.


This thesis is an attempt to understand the physics of short-range entangled phases of fermions through several related approaches. The first angle is topological quantum field theory. We discuss the classification of interacting fermionic short-range entangled phases by spin cobordism and give an algebraic characterization of unoriented equivariant bosonic topological quantum field theories in one spatial dimension. A second tool is tensor network representation. We develop the formalism of fermionic matrix product states and use it to derive the stacking group law for one dimensional symmetry-enriched fermionic short-range entangled phases. We also study its relationship with state sum constructions of topological quantum field theories and develop a state sum construction for pin-minus theories in one spatial dimension. The third approach is topological band theory. We classify free fermionic phases enriched by a unitary symmetry in any dimension and determine the map into the interacting classification.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:topological phases, topological field theory, tensor networks, topological band theory, fermions, entanglement, effective field theory, discrete symmetries, strongly correlated systems, edge states, bosonization, spin chains, lattice models, symmetry protected states, topological superconductors
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:
  • Motrunich, Olexei I. (chair)
  • Chen, Xie
  • Marcolli, Matilde
  • Kapustin, Anton N.
Defense Date:16 May 2019
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Simons Foundation Investigator AwardUNSPECIFIED
Record Number:CaltechTHESIS:05312019-162611521
Persistent URL:
Related URLs:
URLURL TypeDescription adapted for ch.1 adapted for ch.2 adapted for ch.3 adapted for ch.3 adapted for ch.3 adapted for ch.4 adapted for ch.5
Turzillo, Alexander Michael0000-0003-4293-4293
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:11588
Deposited By: Alex Turzillo
Deposited On:06 Jun 2019 19:59
Last Modified:28 Feb 2023 19:16

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