Building models of topological quantum criticality from pivot Hamiltonians
Abstract
Progress in understanding symmetry-protected topological (SPT) phases has been greatly aided by our ability to construct lattice models realizing these states. In contrast, a systematic approach to constructing models that realize quantum critical points between SPT phases is lacking, particularly in dimension d > 1. Here, we show how the recently introduced notion of the pivot Hamiltonian—generating rotations between SPT phases—facilitates such a construction. We demonstrate this approach by constructing a spin model on the triangular lattice, which is midway between a trivial and SPT phase. The pivot Hamiltonian generates a U(1) pivot symmetry which helps to stabilize a direct SPT transition. The sign-problem free nature of the model—with an additional Ising interaction preserving the pivot symmetry—allows us to obtain the phase diagram using quantum Monte Carlo simulations. We find evidence for a direct transition between trivial and SPT phases that is consistent with a deconfined quantum critical point with emergent SO(5) symmetry. The known anomaly of the latter is made possible by the non-local nature of the U(1) pivot symmetry. Interestingly, the pivot Hamiltonian generating this symmetry is nothing other than the staggered Baxter-Wu three-spin interaction. This work illustrates the importance of U(1) pivot symmetries and proposes how to generally construct sign-problem-free lattice models of SPT transitions with such anomalous symmetry groups for other lattices and dimensions.
Additional Information
© 2023 N. Tantivasadakarn et al. This work is licensed under the Creative Commons Attribution 4.0 International License. Published by the SciPost Foundation. NT is supported by NSERC. AV and RV are supported by the Simons Collaboration on UltraQuantum Matter, which is a grant from the Simons Foundation (651440, A.V.). RV is supported by the Harvard Quantum Initiative Postdoctoral Fellowship in Science and Engineering.Attached Files
Published - SciPostPhys_14_2_013.pdf
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Additional details
- Eprint ID
- 120200
- Resolver ID
- CaltechAUTHORS:20230321-821389800.21
- Natural Sciences and Engineering Research Council of Canada (NSERC)
- Simons Foundation
- 651440
- Harvard University
- Created
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2023-05-16Created from EPrint's datestamp field
- Updated
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2023-05-16Created from EPrint's last_modified field
- Caltech groups
- Walter Burke Institute for Theoretical Physics