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Ising ferromagnet to valence bond solid transition in a one-dimensional spin chain - analogies to deconfined quantum critical points

Jiang, Shenghan and Motrunich, Olexei (2019) Ising ferromagnet to valence bond solid transition in a one-dimensional spin chain - analogies to deconfined quantum critical points. Physical Review B, 99 (7). Art. No. 075103. ISSN 2469-9950. http://resolver.caltech.edu/CaltechAUTHORS:20181105-090225094

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Abstract

We study a one-dimensional (1D) system that shows many analogies to proposed two-dimensional (2D) deconfined quantum critical points (DQCP). Our system is a translationally invariant spin-1/2 chain with onsite Z_2×Z_2 symmetry and time-reversal symmetry. It undergoes a direct continuous transition from a ferromagnet (FM), where one of the Z2 symmetries and the time reversal are broken, to a valence bond solid (VBS), where all onsite symmetries are restored while the translation symmetry is broken. The other Z_2 symmetry remains unbroken throughout, but its presence is crucial for both the direct transition (via specific Berry phase effect on topological defects, also related to a Lieb-Schultz-Mattis–type theorem) and the precise characterization of the VBS phase (which has crystalline-symmetry-protected-topological–like property). The transition has a description in terms of either two domain-wall species that “fractionalize” the VBS order parameter or in terms of two partons that “fractionalize” the FM order parameter, with each picture having its own Z_2 gauge theory structure. The two descriptions are dual to each other and, at long wavelengths, take the form of a self-dual gauged Ashkin-Teller model, reminiscent of the self-dual easy-plane noncompact CP^1 model that arises in the description of the 2D easy-plane DQCP. We also find an exact reformulation of the transition that leads to a simple field-theory description that explicitly unifies the FM and VBS order parameters; this reformulation can be interpreted as a new parton approach that does not attempt to fractionalize either of the FM and VBS order parameters but instead encodes them in instanton operators. Aside from providing explicit realizations of many ideas proposed in the context of the 2D DQCP, here in the simpler and fully tractable 1D setting with continuous transition, our study also suggests a possible line of approach to the 2D DQCP.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org./10.1103/PhysRevB.99.075103DOIArticle
https://arxiv.org/abs/1808.07981arXivDiscussion Paper
ORCID:
AuthorORCID
Motrunich, Olexei0000-0001-8031-0022
Additional Information:© 2019 American Physical Society. Received 21 September 2018; revised manuscript received 7 January 2019; published 1 February 2019. The authors would like to thank J. Alicea, Y.-M. Lu, D. Mross, Y. Ran, B. Roberts, and A. Vishwanath for useful discussions. This work was supported by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center, with support of the Gordon and Betty Moore Foundation, and also by NSF through Grant No. DMR-1619696.
Group:IQIM, Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
NSFDMR-1619696
Record Number:CaltechAUTHORS:20181105-090225094
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20181105-090225094
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:90630
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:06 Nov 2018 17:07
Last Modified:01 Feb 2019 19:00

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