Magnetic impurities at quantum critical points: Large- N expansion and connections to symmetry-protected topological states
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PhysRevB.104.104201.pdf
Description
Published version
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987.31 KB
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Author(s)
Liu, Shang
Shapourian, Hassan
Vishwanath, Ashvin
Metlitski, Max A
Date Issued
2021
Journal
Physical Review B
Publisher
American Physical Society (APS)
Citation
Liu, Shang, Shapourian, Hassan, Vishwanath, Ashvin and Metlitski, Max A. 2021. "Magnetic impurities at quantum critical points: Large- N expansion and connections to symmetry-protected topological states." Physical Review B, 104 (10).
Version
Final published version
Abstract
In symmetry protected topological (SPT) phases, the combination of symmetries
and a bulk gap stabilizes protected modes at surfaces or at topological
defects. Understanding the fate of these modes at a quantum critical point,
when the protecting symmetries are on the verge of being broken, is an
outstanding problem. This interplay of topology and criticality must
incorporate both the bulk dynamics of critical points, often described by
nontrivial conformal field theories, and SPT physics. Here, we study the
simplest nontrivial setting - that of a 0+1 dimensional topological mode - a
quantum spin - coupled to a 2+1D critical bulk. Using the large-$N$ technique
we solve a series of models which, as a consequence of topology, demonstrate
intermediate coupling fixed points. We compare our results to previous
numerical simulations and find good agreement. We also point out intriguing
connections to generalized Kondo problems and Sachdev-Ye-Kitaev (SYK) models.
In particular, we show that a Luttinger theorem derived for the complex SYK
models, that relates the charge density to particle-hole asymmetry, also holds
in our setting. These results should help stimulate further analytical study of
the interplay between SPT physics and quantum criticality.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PHYSREVB.104.104201
