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:
- Publication Date:
- 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.
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
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.
@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}
}
https://doi.org/10.1016/j.nuclphysb.2017.03.021
Web of Science
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
Operator content of two-dimensional conformally invariant theories
journal, January 1986
- Cardy, John L.
- Nuclear Physics B, Vol. 270
Two-dimensional critical systems labelled by Dynkin diagrams
journal, January 1987
- Pasquier, Vincent
- Nuclear Physics B, Vol. 285
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
The operator algebra of orbifold models
journal, September 1989
- Dijkgraaf, Robbert; Vafa, Cumrun; Verlinde, Erik
- Communications in Mathematical Physics, Vol. 123, Issue 3
Density matrix formulation for quantum renormalization groups
journal, November 1992
- White, Steven R.
- Physical Review Letters, Vol. 69, Issue 19
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
Rokhsar-Kivelson models of bosonic symmetry-protected topological states
journal, April 2015
- Santos, Luiz H.
- Physical Review B, Vol. 91, Issue 15
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
Discrete symmetries of unitary minimal conformal theories
journal, December 1998
- Ruelle, P.; Verhoeven, O.
- Nuclear Physics B, Vol. 535, Issue 3
Criticality in translation-invariant parafermion chains
journal, March 2015
- Li, Wei; Yang, Shuo; Tu, Hong-Hao
- Physical Review B, Vol. 91, Issue 11
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
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
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
Verma modules over the virasoro algebra
journal, January 1984
- Feigin, B. L.; Fuks, D. B.
- Functional Analysis and Its Applications, Vol. 17, Issue 3