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Title: Gapless Symmetry-Protected Topological Order

Journal Article · · Physical Review. X
 [1];  [1];  [2]
  1. Univ. of California, Berkeley, CA (United States)
  2. Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Univ. of Massachusetts, Amherst, MA (United States)
+ Show Author Affiliations

We introduce exactly solvable gapless quantum systems in d dimensions that support symmetry-protected topological (SPT) edge modes. Our construction leads to long-range entangled, critical points or phases that can be interpreted as critical condensates of domain walls “decorated” with dimension ( d - 1 ) SPT systems. Using a combination of field theory and exact lattice results, we argue that such gapless SPT systems have symmetry-protected topological edge modes that can be either gapless or symmetry broken, leading to unusual surface critical properties. Despite the absence of a bulk gap, these edge modes are robust against arbitrary symmetry-preserving local perturbations near the edges. In two dimensions, we construct wave functions that can also be interpreted as unusual quantum critical points with diffusive scaling in the bulk but ballistic edge dynamics.

Research Organization:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC); USDOE
Grant/Contract Number:
AC02-05CH11231
OSTI ID:
1412946
Alternate ID(s):
OSTI ID: 1485068
Journal Information:
Physical Review. X, Vol. 7, Issue 4; ISSN 2160-3308
Publisher:
American Physical SocietyCopyright Statement
Country of Publication:
United States
Language:
English

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conference January 2009
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Symmetry protection of topological order in one-dimensional quantum spin systems text January 2009
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The density-matrix renormalization group in the age of matrix product states text January 2010
A number conserving theory for topologically protected degeneracy in one-dimensional fermions text January 2011
Symmetry protected topological orders and the group cohomology of their symmetry group text January 2011
Dynamical stability of the quantum Lifshitz theory in 2+1 Dimensions text January 2012
Parafermionic edge zero modes in Z_n-invariant spin chains text January 2012
Quantized topological terms in weak-coupling gauge theories with symmetry and their connection to symmetry enriched topological phases text January 2012
Symmetry protected topological phases from decorated domain walls text January 2013
Area laws in a many-body localized state and its implications for topological order text January 2013
The Hilbert-glass transition: new universality of temperature-tuned many-body dynamical quantum criticality text January 2013
Localization and topology protected quantum coherence at the edge of 'hot' matter preprint January 2013
Wave Function and Strange Correlator of Short Range Entangled states text January 2013
Stability of zero modes in parafermion chains text January 2014
Hidden order and flux attachment in symmetry protected topological phases: a Laughlin-like approach text January 2014
Quantum criticality of hot random spin chains text January 2014
Is the Composite Fermion a Dirac Particle? text January 2015
Discovery of a Weyl Fermion Semimetal and Topological Fermi Arcs text January 2015
Experimental discovery of Weyl semimetal TaAs text January 2015
Quantum Phase Transitions Between a Class of Symmetry Protected Topological States text January 2015
Wavefunctions of Symmetry Protected Topological Phases from Conformal Field Theories text January 2015
The phase transitions between $Z_n\times Z_n$ bosonic topological phases in 1+1 D, and a constraint on the central charge for the critical points between bosonic symmetry protected topological phases text January 2017
Criticality in self-dual sine-Gordon models text January 2002
Topological Order and Conformal Quantum Critical Points text January 2003
Topological invariants of time-reversal-invariant band structures text January 2006
Topological Insulators in Three Dimensions text January 2006
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Cited By (6)

Emergent mode and bound states in single-component one-dimensional lattice fermionic systems journal November 2019
Characterization of Topological States via Dual Multipartite Entanglement journal June 2018
Topologically Protected Long Edge Coherence Times in Symmetry-Broken Phases journal June 2019
Mapping topological to conformal field theories through strange correlators text January 2018
Full Commuting Projector Hamiltonians of Interacting Symmetry-Protected Topological Phases of Fermions text January 2018
Emergent mode and bound states in single-component one-dimensional lattice fermionic systems text January 2018

Figures / Tables (8)

FIG. 1(p. 3)figure FIG. 1
FIG. 2(p. 4)figure FIG. 2
FIG. 3(p. 5)figure FIG. 3
FIG. 4(p. 6)figure FIG. 4
FIG. 5(p. 7)figure FIG. 5
FIG. 6(p. 11)figure FIG. 6
FIG. 7(p. 12)figure FIG. 7
FIG. 8(p. 13)figure FIG. 8

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