skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Many-body topological invariants in fermionic symmetry-protected topological phases: Cases of point group symmetries

Abstract

Not provided.

Authors:
; ;
Publication Date:
Research Org.:
Univ. of Illinois at Urbana-Champaign, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1535923
DOE Contract Number:  
SC0008692
Resource Type:
Journal Article
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 95; Journal Issue: 20; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
Materials Science; Physics

Citation Formats

Shiozaki, Ken, Shapourian, Hassan, and Ryu, Shinsei. Many-body topological invariants in fermionic symmetry-protected topological phases: Cases of point group symmetries. United States: N. p., 2017. Web. doi:10.1103/physrevb.95.205139.
Shiozaki, Ken, Shapourian, Hassan, & Ryu, Shinsei. Many-body topological invariants in fermionic symmetry-protected topological phases: Cases of point group symmetries. United States. doi:10.1103/physrevb.95.205139.
Shiozaki, Ken, Shapourian, Hassan, and Ryu, Shinsei. Mon . "Many-body topological invariants in fermionic symmetry-protected topological phases: Cases of point group symmetries". United States. doi:10.1103/physrevb.95.205139.
@article{osti_1535923,
title = {Many-body topological invariants in fermionic symmetry-protected topological phases: Cases of point group symmetries},
author = {Shiozaki, Ken and Shapourian, Hassan and Ryu, Shinsei},
abstractNote = {Not provided.},
doi = {10.1103/physrevb.95.205139},
journal = {Physical Review B},
issn = {2469-9950},
number = 20,
volume = 95,
place = {United States},
year = {2017},
month = {5}
}

Works referenced in this record:

Classification of topological insulators and superconductors in three spatial dimensions
journal, November 2008


Topological insulators and superconductors: tenfold way and dimensional hierarchy
journal, June 2010


Colloquium: Topological insulators
journal, November 2010


Topological insulators and superconductors
journal, October 2011


Topological BF field theory description of topological insulators
journal, June 2011


Topological phases of fermions in one dimension
journal, February 2011


Twisted Equivariant Matter
journal, March 2013


Classification of Interacting Electronic Topological Insulators in Three Dimensions
journal, February 2014


Fermionic symmetry protected topological phases and cobordisms
journal, December 2015

  • Kapustin, Anton; Thorngren, Ryan; Turzillo, Alex
  • Journal of High Energy Physics, Vol. 2015, Issue 12
  • DOI: 10.1007/JHEP12(2015)052

Global anomalies on the surface of fermionic symmetry-protected topological phases in (3+1) dimensions
journal, February 2016


Fermion path integrals and topological phases
journal, July 2016


State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter
journal, April 2017

  • Bhardwaj, Lakshya; Gaiotto, Davide; Kapustin, Anton
  • Journal of High Energy Physics, Vol. 2017, Issue 4
  • DOI: 10.1007/JHEP04(2017)096

Entanglement spectrum of a topological phase in one dimension
journal, February 2010


Classification of gapped symmetric phases in one-dimensional spin systems
journal, January 2011


Classifying quantum phases using matrix product states and projected entangled pair states
journal, October 2011


Symmetry protected topological orders and the group cohomology of their symmetry group
journal, April 2013


Theory and classification of interacting integer topological phases in two dimensions: A Chern-Simons approach
journal, September 2012


Braiding statistics approach to symmetry-protected topological phases
journal, September 2012


Symmetry-protected topological phases and orbifolds: Generalized Laughlin's argument
journal, August 2013


Nonabelions in the fractional quantum hall effect
journal, August 1991


Fault-tolerant quantum computation by anyons
journal, January 2003


String-net condensation: A physical mechanism for topological phases
journal, January 2005


Anyons in an exactly solved model and beyond
journal, January 2006


Quantum field theory and the Jones polynomial
journal, September 1989

  • Witten, Edward
  • Communications in Mathematical Physics, Vol. 121, Issue 3
  • DOI: 10.1007/BF01217730

State sum invariants of 3-manifolds and quantum 6j-symbols
journal, October 1992


Topological gauge theories and group cohomology
journal, April 1990

  • Dijkgraaf, Robbert; Witten, Edward
  • Communications in Mathematical Physics, Vol. 129, Issue 2
  • DOI: 10.1007/BF02096988

Quantum orders and symmetric spin liquids
journal, April 2002


Classification of symmetry enriched topological phases with exactly solvable models
journal, April 2013


Classifying fractionalization: Symmetry classification of gapped Z 2 spin liquids in two dimensions
journal, March 2013


Theory of twist liquids: Gauging an anyonic symmetry
journal, September 2015


Equivariant topological quantum field theory and symmetry protected topological phases
journal, March 2017


Spin TQFTs and fermionic phases of matter
journal, October 2016

  • Gaiotto, Davide; Kapustin, Anton
  • International Journal of Modern Physics A, Vol. 31, Issue 28n29
  • DOI: 10.1142/S0217751X16450445

Hamiltonian models for topological phases of matter in three spatial dimensions
journal, February 2017


Matrix product states and equivariant topological field theories for bosonic symmetry-protected topological phases in (1+1) dimensions
journal, April 2017


Fermionic matrix product states and one-dimensional topological phases
journal, February 2017


Topological Characterization of Fractional Quantum Hall Ground States from Microscopic Hamiltonians
journal, June 2013


Universal symmetry-protected topological invariants for symmetry-protected topological states
journal, February 2014


Modular matrices as topological order parameter by a gauge-symmetry-preserved tensor renormalization approach
journal, November 2014


Universal Wave-Function Overlap and Universal Topological Data from Generic Gapped Ground States
journal, July 2015


Matrix product operators for symmetry-protected topological phases: Gauging and edge theories
journal, November 2016


Quantum-Mechanical Position Operator in Extended Systems
journal, March 1998


Entanglement entropy and the Berry phase in the solid state
journal, June 2006


Detection of symmetry-protected topological phases in one dimension
journal, September 2012


Detecting two-dimensional symmetry-protected topological order in a ground-state wave function
journal, December 2014


Dai-Freed theorem and topological phases of matter
journal, September 2016


Momentum polarization: An entanglement measure of topological spin and chiral central charge
journal, November 2013


Many-Body Topological Invariants for Fermionic Symmetry-Protected Topological Phases
journal, May 2017


Spatial reflection and associated string order in quantum spin chains
journal, October 2009


Topological Phases Protected by Point Group Symmetry
journal, February 2017


General Relationship between the Entanglement Spectrum and the Edge State Spectrum of Topological Quantum States
journal, May 2012


Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures
journal, January 1997


Unpaired Majorana fermions in quantum wires
journal, October 2001


Exact ground states and topological order in interacting Kitaev/Majorana chains
journal, September 2015


Topological Criticality in the Chiral-Symmetric AIII Class at Strong Disorder
journal, July 2014


AIII and BDI topological systems at strong disorder
journal, June 2014


Theory of the Topological Anderson Insulator
journal, November 2009


Disorder-induced quantum phase transitions in three-dimensional topological insulators and superconductors
journal, April 2012


Disordered Weak and Strong Topological Insulators
journal, June 2013


Chern-Simons-Witten invariants of lens spaces and torus bundles, and the semiclassical approximation
journal, July 1992

  • Jeffrey, Lisa C.
  • Communications in Mathematical Physics, Vol. 147, Issue 3
  • DOI: 10.1007/BF02097243

Edge modes, edge currents, and gauge invariance in p x + i p y superfluids and superconductors
journal, May 2004


Topological Entanglement Entropy
journal, March 2006


Detecting Topological Order in a Ground State Wave Function
journal, March 2006


Characterization of two-dimensional fermionic insulating states
journal, December 2006


Topological entanglement entropy of Z 2 spin liquids and lattice Laughlin states
journal, August 2011


Interacting topological phases and modular invariance
journal, June 2012


Effect of interactions on two-dimensional fermionic symmetry-protected topological phases with Z 2 symmetry
journal, May 2014


Topology of crystalline insulators and superconductors
journal, October 2014


Symmetry-protected topological states of interacting fermions and bosons
journal, December 2014


The eta invariant, Pin c bordism, and equivariant Spin c bordism for cyclic 2-groups
journal, January 1987


Bulk topological invariants in noninteracting point group symmetric insulators
journal, September 2012


Breakdown of the topological classification Z for gapped phases of noninteracting fermions by quartic interactions
journal, September 2015


Spherical topological insulator
journal, December 2012


Relativistic Landau models and generation of fuzzy spheres
journal, July 2016


Operator content and modular properties of higher-dimensional conformal field theories
journal, December 1991


Entanglement entropy of gapped phases and topological order in three dimensions
journal, November 2011


Topological field theory of time-reversal invariant insulators
journal, November 2008

  • Qi, Xiao-Liang; Hughes, Taylor L.; Zhang, Shou-Cheng
  • Physical Review B, Vol. 78, Issue 19, Article No. 195424
  • DOI: 10.1103/PhysRevB.78.195424

Interacting fermionic topological insulators/superconductors in three dimensions
journal, May 2014


Confinement of quarks
journal, October 1974


On the eigenfunctions of the Dirac operator on spheres and real hyperbolic spaces
journal, September 1996


Algorithm 923: Efficient Numerical Computation of the Pfaffian for Dense and Banded Skew-Symmetric Matrices
journal, August 2012


Riemann surfaces and spin structures
journal, January 1971

  • Atiyah, Michael F.
  • Annales scientifiques de l'École normale supérieure, Vol. 4, Issue 1
  • DOI: 10.24033/asens.1205

Spin Structures and Quadratic forms on Surfaces
journal, October 1980


Dimers on Graphs in Non-Orientable Surfaces
journal, January 2009


Dimers on Surface Graphs and Spin Structures. I
journal, July 2007

  • Cimasoni, David; Reshetikhin, Nicolai
  • Communications in Mathematical Physics, Vol. 275, Issue 1
  • DOI: 10.1007/s00220-007-0302-7

Equivariant K-theory
journal, January 1968

  • Segal, Graeme
  • Publications mathématiques de l'IHÉS, Vol. 34, Issue 1
  • DOI: 10.1007/BF02684593