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Scaling and diffusion of Dirac composite fermions

Lee, Chao-Jung and Mulligan, Michael (2020) Scaling and diffusion of Dirac composite fermions. Physical Review Research, 2 (2). Art. No. 023303. ISSN 2643-1564. https://resolver.caltech.edu/CaltechAUTHORS:20200224-110724526

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Abstract

We study the effects of quenched disorder and a dissipative Coulomb interaction on an anyon gas in a periodic potential undergoing a quantum phase transition. We use a (2+1)−dimensional low-energy effective description that involves Nf=1 Dirac fermion coupled to a U(1) Chern-Simons gauge field at level (θ−1/2). When θ=1/2 the anyons are free Dirac fermions that exhibit an integer quantum Hall transition; when θ=1 the anyons are bosons undergoing a superconductor-insulator transition in the universality class of the three-dimensional XY model. Using the large Nf approximation we perform a renormalization-group analysis. We find the Coulomb interaction to be an irrelevant perturbation of the clean fixed point for any θ. The dissipative Coulomb interaction allows for two classes of IR stable fixed points in the presence of disorder: those with a finite nonzero Coulomb coupling and dynamical critical exponent z=1 and those with an effectively infinite Coulomb coupling and 1<z<2. At θ=1/2 the clean fixed point is stable to charge-conjugation preserving (random mass) disorder, while a line of diffusive fixed points is obtained when the product of charge-conjugation and time-reversal symmetries is preserved. At θ=1 we find a finite disorder fixed point with unbroken charge-conjugation symmetry whether or not the Coulomb interaction is present. Other cases result in runaway flows. We comment on the relation of our results to other theoretical studies and the relevancy to experiment.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevResearch.2.023303DOIArticle
https://arxiv.org/abs/1912.12303arXivDiscussion Paper
ORCID:
AuthorORCID
Lee, Chao-Jung0000-0003-3339-1522
Additional Information:© 2020 Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Received 29 January 2020; accepted 25 March 2020; published 8 June 2020. We thank Hart Goldman, Sri Raghu, and Alex Thomson for useful conversations and correspondence. This material is based upon work supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences under Grant No. DE-SC0020007. This research was supported in part by the National Science Foundation under Grant No. NSF PHY-1748958.
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0020007
NSFPHY-1748958
Issue or Number:2
Record Number:CaltechAUTHORS:20200224-110724526
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200224-110724526
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:101492
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:24 Feb 2020 19:18
Last Modified:17 Aug 2020 20:37

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