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Title: The phase transitions between Z n × Z n 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 in this paper 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:
 [1];  [1];  [2];  [3]
  1. Univ. of California, Berkeley, CA (United States). Dept. of Physics
  2. SLAC National Accelerator Lab., Menlo Park, CA (United States). Stanford Institute for Materials and Energy Science (SIMES)
  3. Univ. of California, Berkeley, CA (United States). Dept. of Physics; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Materials Sciences Division
Publication Date:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1349311
Alternate Identifier(s):
OSTI ID: 1369421; OSTI ID: 1413729
Grant/Contract Number:
AC02-05CH11231; AC02-76SF00515
Resource Type:
Journal Article: Published Article
Journal Name:
Nuclear Physics. B
Additional Journal Information:
Journal Volume: 919; Journal Issue: C; Journal ID: ISSN 0550-3213
Publisher:
Elsevier
Country of Publication:
United States
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 Zn × Zn bosonic topological phases in 1 + 1D, and a constraint on the central charge for the critical points between bosonic symmetry protected topological phases. United States: 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 Zn × Zn bosonic topological phases in 1 + 1D, and a constraint on the central charge for the critical points between bosonic symmetry protected topological phases. United States. doi:10.1016/j.nuclphysb.2017.03.021.
Tsui, Lokman, Huang, Yen-Ta, Jiang, Hong-Chen, and Lee, Dung-Hai. Mon . "The phase transitions between Zn × Zn bosonic topological phases in 1 + 1D, and a constraint on the central charge for the critical points between bosonic symmetry protected topological phases". United States. doi:10.1016/j.nuclphysb.2017.03.021.
@article{osti_1349311,
title = {The phase transitions between Zn × Zn 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 in this paper we study a specific class of such phase transitions in 1+1 dimensions – the phase transition between bosonic topological phases protected by Zn × Zn. 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 = {United States},
year = {Mon Mar 27 00:00:00 EDT 2017},
month = {Mon Mar 27 00:00:00 EDT 2017}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1016/j.nuclphysb.2017.03.021

Citation Metrics:
Cited by: 4works
Citation information provided by
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  • 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 in this paper 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 transitionmore » 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.« less
  • 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 othermore » 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.« less
  • The subject of this paper is the phase transition between symmetry protected topological states (SPTs). We consider spatial dimension d and symmetry group G so that the cohomology group, Hd+1(G,U(1)), contains at least one Z2n or Z factor. We show that the phase transition between the trivial SPT and the root states that generate the Z2n or Z groups can be induced on the boundary of a (d+1)-dimensional View the MathML source-symmetric SPT by a View the MathML source symmetry breaking field. Moreover we show these boundary phase transitions can be “transplanted” to d dimensions and realized in lattice modelsmore » as a function of a tuning parameter. The price one pays is for the critical value of the tuning parameter there is an extra non-local (duality-like) symmetry. In the case where the phase transition is continuous, our theory predicts the presence of unusual (sometimes fractionalized) excitations corresponding to delocalized boundary excitations of the non-trivial SPT on one side of the transition. This theory also predicts other phase transition scenarios including first order transition and transition via an intermediate symmetry breaking phase.« less
  • The subject of this paper is the phase transition between symmetry protected topological states (SPTs). We consider spatial dimension d and symmetry group G so that the cohomology group, H d+1(G,U(1)), contains at least one Z 2n or Z factor. We show that the phase transition between the trivial SPT and the root states that generate the Z 2n or Z groups can be induced on the boundary of a (d+1)-dimensional G x Z T 2-symmetric SPT by a Z T 2 symmetry breaking field. Moreover we show these boundary phase transitions can be “transplanted” to d dimensions and realizedmore » in lattice models as a function of a tuning parameter. The price one pays is for the critical value of the tuning parameter there is an extra non-local (duality-like) symmetry. In the case where the phase transition is continuous, our theory predicts the presence of unusual (sometimes fractionalized) excitations corresponding to delocalized boundary excitations of the non-trivial SPT on one side of the transition. This theory also predicts other phase transition scenarios including first order transition and transition via an intermediate symmetry breaking phase.« less
  • The subject of this paper is the phase transition between symmetry protected topological states (SPTs). We consider spatial dimension d and symmetry group G so that the cohomology group, H d+1(G,U(1)), contains at least one Z 2n or Z factor. We show that the phase transition between the trivial SPT and the root states that generate the Z 2n or Z groups can be induced on the boundary of a (d+1)-dimensional G x Z T 2-symmetric SPT by a Z T 2 symmetry breaking field. Moreover we show these boundary phase transitions can be “transplanted” to d dimensions and realizedmore » in lattice models as a function of a tuning parameter. The price one pays is for the critical value of the tuning parameter there is an extra non-local (duality-like) symmetry. In the case where the phase transition is continuous, our theory predicts the presence of unusual (sometimes fractionalized) excitations corresponding to delocalized boundary excitations of the non-trivial SPT on one side of the transition. This theory also predicts other phase transition scenarios including first order transition and transition via an intermediate symmetry breaking phase.« less