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Infinite randomness with continuously varying critical exponents in the random XYZ spin chain

Roberts, Brenden and Motrunich, Olexei I. (2021) Infinite randomness with continuously varying critical exponents in the random XYZ spin chain. Physical Review B, 104 (21). Art. No. 214208. ISSN 2469-9950. doi:10.1103/PhysRevB.104.214208.

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We study the antiferromagnetic XYZ spin chain with quenched bond randomness, focusing on a critical line between localized Ising magnetic phases. A previous calculation using the spectrum-bifurcation renormalization group, and assuming marginal many-body localization, proposed that critical indices vary continuously. In this work, we solve the low-energy physics using an unbiased numerically exact tensor network method named the “rigorous renormalization group.” We find a line of fixed points consistent with infinite-randomness phenomenology, with indeed continuously varying critical exponents for average spin correlations. A self-consistent Hartree–Fock-type treatment of the z couplings as interactions added to the free-fermion random XY model captures much of the important physics including the varying exponents; we provide an understanding of this as a result of local correlation induced between the mean-field couplings. We solve the problem of the locally correlated XY spin chain with an arbitrary degree of correlation and provide analytical strong-disorder renormalization group proofs of continuously varying exponents based on an associated classical random walk problem. This is also an example of a line of fixed points with continuously varying exponents in the equivalent disordered free-fermion chain. We argue that this line of fixed points also controls an extended region of the critical interacting XYZ spin chain.

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Motrunich, Olexei I.0000-0001-8031-0022
Additional Information:© 2021 American Physical Society. Received 20 September 2021; revised 15 December 2021; accepted 15 December 2021; published 27 December 2021. We acknowledge helpful discussions with Jason Alicea, Matteo Ippoliti, Cheng-Ju Lin, Sanjay Moudgalya, Gil Refael, Kevin Slagle, and Christopher White. We are also grateful for earlier collaboration with Thomas Vidick on the RRG which led us to look for new applications of this method. O.M. is also grateful for previous collaborations with Kedar Damle, David Huse, and Daniel Fisher on the IRFPs which provided important background for this project. This work was supported by National Science Foundation through Grant No. DMR-2001186. Part of this work was performed at Aspen Center for Physics, which is supported by National Science Foundation Grant No. PHY-1607611.
Group:Institute for Quantum Information and Matter
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Issue or Number:21
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ID Code:110660
Deposited By: George Porter
Deposited On:01 Sep 2021 14:24
Last Modified:04 Jan 2022 19:58

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