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Title: Gapless Symmetry-Protected Topological Order

Abstract

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.

Authors:
; ;
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1412946
Alternate Identifier(s):
OSTI ID: 1485068
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Published Article
Journal Name:
Physical Review. X
Additional Journal Information:
Journal Name: Physical Review. X Journal Volume: 7 Journal Issue: 4; Journal ID: ISSN 2160-3308
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats

Scaffidi, Thomas, Parker, Daniel E., and Vasseur, Romain. Gapless Symmetry-Protected Topological Order. United States: N. p., 2017. Web. doi:10.1103/PhysRevX.7.041048.
Scaffidi, Thomas, Parker, Daniel E., & Vasseur, Romain. Gapless Symmetry-Protected Topological Order. United States. doi:10.1103/PhysRevX.7.041048.
Scaffidi, Thomas, Parker, Daniel E., and Vasseur, Romain. Wed . "Gapless Symmetry-Protected Topological Order". United States. doi:10.1103/PhysRevX.7.041048.
@article{osti_1412946,
title = {Gapless Symmetry-Protected Topological Order},
author = {Scaffidi, Thomas and Parker, Daniel E. and Vasseur, Romain},
abstractNote = {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.},
doi = {10.1103/PhysRevX.7.041048},
journal = {Physical Review. X},
number = 4,
volume = 7,
place = {United States},
year = {2017},
month = {11}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1103/PhysRevX.7.041048

Citation Metrics:
Cited by: 7 works
Citation information provided by
Web of Science

Figures / Tables:

FIG. 1 FIG. 1: Representative states of each order in the 2d example. (a) Trivial: Paramagnetic spins on a triangular lattice with fluctuating domain walls. (b) SPT: Decorating the domain walls, giving a SPTwith a c = 1 edge mode. (c) Gapless trivial: Tuning the domain walls to criticality by restricting themmore » to fully packed loop configurations (defined below), closing the gap and giving a c = 1 edge mode. (d) Doing both yields a gapless SPT with c = 1 + 1 = 2 edge modes.« less

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    Works referencing / citing this record:

    Topologically Protected Long Edge Coherence Times in Symmetry-Broken Phases
    journal, June 2019


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