Gapless SymmetryProtected Topological Order
We introduce exactly solvable gapless quantum systems in d dimensions that support symmetryprotected topological (SPT) edge modes. Our construction leads to longrange 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 symmetryprotected 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 symmetrypreserving 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:

^{[1]};
^{[1]};
^{[2]}
 Univ. of California, Berkeley, CA (United States)
 Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Univ. of Massachusetts, Amherst, MA (United States)
 Publication Date:
 Grant/Contract Number:
 AC0205CH11231
 Type:
 Accepted Manuscript
 Journal Name:
 Physical Review. X
 Additional Journal Information:
 Journal Volume: 7; Journal Issue: 4; Journal ID: ISSN 21603308
 Publisher:
 American Physical Society
 Research Org:
 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
 Sponsoring Org:
 USDOE Office of Science (SC)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
 OSTI Identifier:
 1485068
Scaffidi, Thomas, Parker, Daniel E., and Vasseur, Romain. Gapless SymmetryProtected Topological Order. United States: N. p.,
Web. doi:10.1103/physrevx.7.041048.
Scaffidi, Thomas, Parker, Daniel E., & Vasseur, Romain. Gapless SymmetryProtected Topological Order. United States. doi:10.1103/physrevx.7.041048.
Scaffidi, Thomas, Parker, Daniel E., and Vasseur, Romain. 2017.
"Gapless SymmetryProtected Topological Order". United States.
doi:10.1103/physrevx.7.041048. https://www.osti.gov/servlets/purl/1485068.
@article{osti_1485068,
title = {Gapless SymmetryProtected 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 symmetryprotected topological (SPT) edge modes. Our construction leads to longrange 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 symmetryprotected 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 symmetrypreserving 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}
}
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