Superuniversality from disorder at two-dimensional topological phase transitions

Byungmin Kang, S. A. Parameswaran, Andrew C. Potter, Romain Vasseur, Snir Gazit

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We investigate the effects of quenched randomness on topological quantum phase transitions in strongly interacting two-dimensional systems. We focus first on transitions driven by the condensation of a subset of fractionalized quasiparticles ("anyons") identified with "electric charge"excitations of a phase with intrinsic topological order. All other anyons have nontrivial mutual statistics with the condensed subset and hence become confined at the anyon condensation transition. Using a combination of microscopically exact duality transformations and asymptotically exact real-space renormalization group techniques applied to these two-dimensional disordered gauge theories, we argue that the resulting critical scaling behavior is "superuniversal"across a wide range of such condensation transitions and is controlled by the same infinite-randomness fixed point as that of the 2D random transverse-field Ising model. We validate this claim using large-scale quantum Monte Carlo simulations that allow us to extract zero-temperature critical exponents and correlation functions in (2+1)D disordered interacting systems. We discuss generalizations of these results to a large class of ground-state and excited-state topological transitions in systems with intrinsic topological order as well as those where topological order is either protected or enriched by global symmetries. When the underlying topological order and the symmetry group are Abelian, our results provide prototypes for topological phase transitions between distinct many-body localized phases.

Original languageAmerican English
Article number224204
JournalPhysical Review B
Issue number22
StatePublished - 28 Dec 2020

Bibliographical note

Funding Information:
We acknowledge D. Huse for a correspondence on excited-state criticality. B.K. is supported by KIAS Individual Grant PG069402 at the Korea Institute for Advanced Study and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF-2020R1F1A1075569). S.A.P. acknowledges support from the European Research Council (ERC) under the European Union Horizon 2020 Research and Innovation Programme (Grant Agreement No. 804213-TMCS), from EPSRC Grant EP/S020527/1, and from the U.S. National Science Foundation Grant DMR-1455366 during the early stages of this project. R.V. is supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, under Early Career Award No. DE-SC0019168, and the Sloan Foundation through a Sloan Research Fellowship. A.P. is supported by NSF DMR-1653007. S.G. acknowledges support from the Israel Science Foundation, Grant No. 1686/18. Computational resources were provided by the KISTI National Supercomputing Center (KSC-2019-CRE-0187) and the Intel Labs Academic Compute Environment.

Publisher Copyright:
© 2020 American Physical Society.


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