The phase transitions between Z×Z bosonic topological phases in 1 + 1D, and a constraint on the central charge for the critical points between bosonic symmetry protected topological phases

Tsui, Lokman; Huang, Yen-Ta; Jiang, Hong-Chen; Lee, Dung-Hai

doi:10.1016/j.nuclphysb.2017.03.021

Title: The phase transitions between Z×Z bosonic topological phases in 1 + 1D, and a constraint on the central charge for the critical points between bosonic symmetry protected topological phases

Abstract

The study of continuous phase transitions triggered by spontaneous symmetry breaking has brought revolutionary ideas to physics. Recently, through the discovery of symmetry protected topological phases, it is realized that continuous quantum phase transition can also occur between states with the same symmetry but different topology. Here we study a specific class of such phase transitions in 1+1 dimensions – the phase transition between bosonic topological phases protected by Z n ×Z n . We find in all cases the critical point possesses two gap opening relevant operators: one leads to a Landau-forbidden symmetry breaking phase transition and the other to the topological phase transition. We also obtained a constraint on the central charge for general phase transitions between symmetry protected bosonic topological phases in 1+1D.

Authors:: Tsui, Lokman; Huang, Yen-Ta; Jiang, Hong-Chen; Lee, Dung-Hai

Publication Date:: Thu Jun 01 00:00:00 EDT 2017

Research Org.:: SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

OSTI Identifier:: 1349311

Alternate Identifier(s):: OSTI ID: 1369421; OSTI ID: 1413729

Grant/Contract Number:: AC02-05CH11231; AC02-76SF00515

Resource Type:: Published Article

Journal Name:: Nuclear Physics. B

Additional Journal Information:: Journal Name: Nuclear Physics. B Journal Volume: 919 Journal Issue: C; Journal ID: ISSN 0550-3213

Publisher:: Elsevier

Country of Publication:: Netherlands

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Tsui, Lokman, Huang, Yen-Ta, Jiang, Hong-Chen, and Lee, Dung-Hai. The phase transitions between Z×Z bosonic topological phases in 1 + 1D, and a constraint on the central charge for the critical points between bosonic symmetry protected topological phases.  Netherlands: N. p., 2017. 
Web.  doi:10.1016/j.nuclphysb.2017.03.021.

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                    Tsui, Lokman, Huang, Yen-Ta, Jiang, Hong-Chen, & Lee, Dung-Hai. The phase transitions between Z×Z bosonic topological phases in 1 + 1D, and a constraint on the central charge for the critical points between bosonic symmetry protected topological phases.  Netherlands.  https://doi.org/10.1016/j.nuclphysb.2017.03.021

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                    Tsui, Lokman, Huang, Yen-Ta, Jiang, Hong-Chen, and Lee, Dung-Hai. Thu .  
"The phase transitions between Z×Z bosonic topological phases in 1 + 1D, and a constraint on the central charge for the critical points between bosonic symmetry protected topological phases".  Netherlands.  https://doi.org/10.1016/j.nuclphysb.2017.03.021.

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@article{osti_1349311,

  title        = {The phase transitions between Z×Z bosonic topological phases in 1 + 1D, and a constraint on the central charge for the critical points between bosonic symmetry protected topological phases},

  author       = {Tsui, Lokman and Huang, Yen-Ta and Jiang, Hong-Chen and Lee, Dung-Hai},

  abstractNote = {The study of continuous phase transitions triggered by spontaneous symmetry breaking has brought revolutionary ideas to physics. Recently, through the discovery of symmetry protected topological phases, it is realized that continuous quantum phase transition can also occur between states with the same symmetry but different topology. Here we study a specific class of such phase transitions in 1+1 dimensions – the phase transition between bosonic topological phases protected by Z n ×Z n . We find in all cases the critical point possesses two gap opening relevant operators: one leads to a Landau-forbidden symmetry breaking phase transition and the other to the topological phase transition. We also obtained a constraint on the central charge for general phase transitions between symmetry protected bosonic topological phases in 1+1D.},

  doi          = {10.1016/j.nuclphysb.2017.03.021},

  journal      = {Nuclear Physics. B},

  number       = C,

  volume       = 919,

  place        = {Netherlands},

  year         = {Thu Jun 01 00:00:00 EDT 2017},

  month        = {Thu Jun 01 00:00:00 EDT 2017}

}

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Works referenced in this record:

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

Schnyder, Andreas P.; Ryu, Shinsei; Furusaki, Akira
Physical Review B, Vol. 78, Issue 19
DOI: 10.1103/PhysRevB.78.195125

Operator content of two-dimensional conformally invariant theories
journal, January 1986

Cardy, John L.
Nuclear Physics B, Vol. 270
DOI: 10.1016/0550-3213(86)90552-3

Two-dimensional critical systems labelled by Dynkin diagrams
journal, January 1987

Pasquier, Vincent
Nuclear Physics B, Vol. 285
DOI: 10.1016/0550-3213(87)90332-4

Renormalization, vortices, and symmetry-breaking perturbations in the two-dimensional planar model
journal, August 1977

José, Jorge V.; Kadanoff, Leo P.; Kirkpatrick, Scott
Physical Review B, Vol. 16, Issue 3
DOI: 10.1103/PhysRevB.16.1217

The operator algebra of orbifold models
journal, September 1989

Dijkgraaf, Robbert; Vafa, Cumrun; Verlinde, Erik
Communications in Mathematical Physics, Vol. 123, Issue 3
DOI: 10.1007/BF01238812

Density matrix formulation for quantum renormalization groups
journal, November 1992

White, Steven R.
Physical Review Letters, Vol. 69, Issue 19
DOI: 10.1103/PhysRevLett.69.2863

Quantum phase transitions between a class of symmetry protected topological states
journal, July 2015

Tsui, Lokman; Jiang, Hong-Chen; Lu, Yuan-Ming
Nuclear Physics B, Vol. 896
DOI: 10.1016/j.nuclphysb.2015.04.020

Rokhsar-Kivelson models of bosonic symmetry-protected topological states
journal, April 2015

Santos, Luiz H.
Physical Review B, Vol. 91, Issue 15
DOI: 10.1103/PhysRevB.91.155150

Periodic table for topological insulators and superconductors
conference, January 2009

Kitaev, Alexei; Lebedev, Vladimir; Feigel’man, Mikhail
ADVANCES IN THEORETICAL PHYSICS: Landau Memorial Conference, AIP Conference Proceedings
DOI: 10.1063/1.3149495

Discrete symmetries of unitary minimal conformal theories
journal, December 1998

Ruelle, P.; Verhoeven, O.
Nuclear Physics B, Vol. 535, Issue 3
DOI: 10.1016/S0550-3213(98)00639-7

Criticality in translation-invariant parafermion chains
journal, March 2015

Li, Wei; Yang, Shuo; Tu, Hong-Hao
Physical Review B, Vol. 91, Issue 11
DOI: 10.1103/PhysRevB.91.115133

Infinite conformal symmetry in two-dimensional quantum field theory
journal, July 1984

Belavin, A. A.; Polyakov, A. M.; Zamolodchikov, A. B.
Nuclear Physics B, Vol. 241, Issue 2
DOI: 10.1016/0550-3213(84)90052-X

Lattice derivation of modular invariant partition functions on the torus
journal, December 1987

Pasquier, V.
Journal of Physics A: Mathematical and General, Vol. 20, Issue 18
DOI: 10.1088/0305-4470/20/18/003

Critical behavior and associated conformal algebra of the Z3 potts model
journal, March 1984

Dotsenko, Vl. S.
Journal of Statistical Physics, Vol. 34, Issue 5-6
DOI: 10.1007/BF01009440

Verma modules over the virasoro algebra
journal, January 1984

Feigin, B. L.; Fuks, D. B.
Functional Analysis and Its Applications, Vol. 17, Issue 3
DOI: 10.1007/BF01078118

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Title: The phase transitions between Z×Z bosonic topological phases in 1 + 1D, and a constraint on the central charge for the critical points between bosonic symmetry protected topological phases

Abstract

Citation Formats

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

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Renormalization, vortices, and symmetry-breaking perturbations in the two-dimensional planar model journal, August 1977

The operator algebra of orbifold models journal, September 1989

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Criticality in translation-invariant parafermion chains journal, March 2015

Infinite conformal symmetry in two-dimensional quantum field theory journal, July 1984

Lattice derivation of modular invariant partition functions on the torus journal, December 1987

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Verma modules over the virasoro algebra journal, January 1984

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

Operator content of two-dimensional conformally invariant theories
journal, January 1986

Two-dimensional critical systems labelled by Dynkin diagrams
journal, January 1987

Renormalization, vortices, and symmetry-breaking perturbations in the two-dimensional planar model
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The operator algebra of orbifold models
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journal, April 2015

Periodic table for topological insulators and superconductors
conference, January 2009

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Criticality in translation-invariant parafermion chains
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Infinite conformal symmetry in two-dimensional quantum field theory
journal, July 1984

Lattice derivation of modular invariant partition functions on the torus
journal, December 1987

Critical behavior and associated conformal algebra of the Z3 potts model
journal, March 1984

Verma modules over the virasoro algebra
journal, January 1984