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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. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20210831-203949345

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Abstract

We study the antiferromagnetic XYZ spin chain with quenched randomness, focusing on a critical line between localized Ising magnetic phases. A previous calculation of Slagle et al., Phys. Rev. B 94, 014205 (2016), using the spectrum-bifurcation renormalization group and assuming marginal many-body localization, proposed that critical indices for Edwards-Anderson correlators 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 critical exponents for average spin correlations varying continuously. The phase boundary tunes from a free-fermion fixed point to an S3-symmetric multicritical point. For weak microscopic interactions, a self-consistent Hartree-Fock-type treatment 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 then solve the problem of the locally-correlated XY spin chain with arbitrary degree of correlation and provide analytical strong-disorder renormalization group proofs of continuously varying exponents based on the survival probability of 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. Finally, we conjecture that this line of fixed points also controls the critical XYZ spin chain for small interaction strength.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/2107.12937arXivDiscussion Paper
ORCID:
AuthorORCID
Motrunich, Olexei I.0000-0001-8031-0022
Additional Information:Attribution 4.0 International (CC BY 4.0) 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 DMR-2001186. Part of this work was performed at Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1607611.
Group:Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
NSFDMR-2001186
NSFPHY-1607611
Record Number:CaltechAUTHORS:20210831-203949345
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210831-203949345
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:110660
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:01 Sep 2021 14:24
Last Modified:01 Sep 2021 14:24

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