Gapless Symmetry-Protected Topological Order
By Thomas Scaffidi, D. Parker, Romain Vasseur. 2017
149 citations recorded by the source corpus.
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 wavefunctions that can also be interpreted as unusual quantum critical points with diffusive scaling in the bulk but ballistic edge dynamics.
Subfields: Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/a7eb86bc8cbdfb493243cd8a905496635fd41252
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In Atomic and Molecular Physics, and Optics
- R. Verresen
- Ryan Thorngren
- Frank Pollmann
- Tibor Rakovszky
- N. G. Jones
- Michael Jason Knap
- Yifan Wang
- Pablo Sala
Citations in the corpus
- Fusion Category Symmetry I: Anomaly In-Flow and Gapped Phases (2019, methodology): “This theory may also be obtained by applying the Z(2)2 SPT entangler to the Ising(2) Hamiltonian, similar in spirit to the decorated domain walls of [46].”
- Statistical localization: From strong fragmentation to strong edge modes (2019, background): “Recently, frameworks for gapless topological phases have been introduced [87, 88].”
- Gapless Topological Phases and Symmetry-Enriched Quantum Criticality (2019, methodology): “[28] showed that the edges mode of the cluster SPT phase (|J | < 1) persist at the Ising critical point at |J | = 1 (beyond which there is a phase that spontaneously breaks PA), although no bulk invariant was identified.”