Title: Fermionic symmetry protected topological phases and cobordisms

Journal Article · · Journal of High Energy Physics (Online)
 [1];  [2];  [3];  [3]
  1. California Inst. of Technology (CalTech), Pasadena, CA (United States); Caltech
  2. Univ. of California, Berkeley, CA (United States)
  3. California Inst. of Technology (CalTech), Pasadena, CA (United States)
+ Show Author Affiliations

It has been proposed recently that interacting Symmetry Protected Topological Phases can be classified using cobordism theory. We test this proposal in the case of Fermionic SPT phases with \( {\mathrm{\mathbb{Z}}}_2 \) symmetry, where \( {\mathrm{\mathbb{Z}}}_2 \) is either time-reversal or an internal symmetry. We find that cobordism classification correctly describes all known Fermionic SPT phases in space dimension D ≤ 3 and also predicts that all such phases can be realized by free fermions. In higher dimensions we predict the existence of inherently interacting fermionic SPT phases

Research Organization:
California Inst. of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
Grant/Contract Number:
FG02-92ER40701; SC0011632
OSTI ID:
1599360
Journal Information:
Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 12 Vol. 2015; ISSN 1029-8479
Publisher:
Springer BerlinCopyright Statement
Country of Publication:
United States
Language:
English

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Computational Power of Symmetry-Protected Topological Phases text January 2016
Classification and surface anomaly of glide symmetry protected topological phases in three dimensions text January 2017
Anomaly Manifestation of Lieb-Schultz-Mattis Theorem and Topological Phases text January 2017
Symmetric Gapped Interfaces of SPT and SET States: Systematic Constructions text January 2017
Loop Braiding Statistics and Interacting Fermionic Symmetry-Protected Topological Phases in Three Dimensions text January 2017
Dimensional Reduction and Topological Invariants of Symmetry-Protected Topological Phases text January 2017
Many-body topological invariants for fermionic short-range entangled topological phases protected by antiunitary symmetries text January 2017
Global Symmetries, Counterterms, and Duality in Chern-Simons Matter Theories with Orthogonal Gauge Groups text January 2017
Why are fractional charges of orientifolds compatible with Dirac quantization? text January 2018
Full Commuting Projector Hamiltonians of Interacting Symmetry-Protected Topological Phases of Fermions text January 2018
Remarks on the Green-Schwarz terms of six-dimensional supergravity theories text January 2018
Free and Interacting Short-Range Entangled Phases of Fermions: Beyond the Ten-Fold Way text January 2018
Crystalline topological phases as defect networks text January 2018
Choreographed entangle dances: topological states of quantum matter text January 2019
Translation constraints on quantum phases with twisted boundary conditions text January 2019
Ground-state degeneracy of non-Abelian topological phases from coupled wires text January 2019

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