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Title: Quantum phase transitions between a class of symmetry protected topological states

Journal Article · · Nuclear Physics. B
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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 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.

Research Organization:
SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
DOE Contract Number:
AC02-76SF00515
OSTI ID:
1335086
Report Number(s):
SLAC-PUB-16748; arXiv:1503.06794
Journal Information:
Nuclear Physics. B, Vol. 896, Issue C; ISSN 0550-3213
Publisher:
Elsevier
Country of Publication:
United States
Language:
English

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Cited By (15)

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One-dimensional symmetry protected topological phases and their transitions journal October 2017
Anomalies and entanglement renormalization journal September 2017
UV perspective on mixed anomalies at critical points between bosonic symmetry-protected phases journal October 2019
A multi-orbital iterated perturbation theory for model Hamiltonians and real material-specific calculations of correlated systems journal September 2016
Gapless Symmetry-Protected Topological Order journal November 2017
Detecting and identifying two-dimensional symmetry-protected topological, symmetry-breaking, and intrinsic topological phases with modular matrices via tensor-network methods journal April 2016
Gapless Symmetry Protected Topological Order text January 2017
One-Dimensional Symmetry Protected Topological Phases and their Transitions text January 2017
A UV perspective on mixed anomalies at critical points between bosonic symmetry-protected phases text January 2019
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 journal June 2017
A holographic theory for the phase transitions between fermionic symmetry-protected topological states journal December 2019
Evidence for deconfined U ( 1 ) gauge theory at the transition between toric code and double semion journal April 2021
Detection of gapped phases of a 1D spin chain with onsite and spatial symmetries text January 2016
From trivial to topological paramagnets: The case of $\mathbb{Z}_2$ and $\mathbb{Z}_2^3$ symmetries in two dimensions text January 2020

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