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


Not provided.

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