Filling constraints on translation invariant dipole conserving systems
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1.
University of Minnesota
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2.
California Institute of Technology
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3.
Technical University of Munich
- 4. Munich Center for Quantum Science and Technology
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5.
Institute for Advanced Study
Abstract
Systems with conserved dipole moment have drawn considerable interest in light of their realization in recent experiments on tilted optical lattices. An important issue regarding such systems is delineating the conditions under which they admit a unique gapped ground state that is consistent with all symmetries. Here, we study one-dimensional translation-invariant lattices that conserve U(1) charge and ℤ𝐿 dipole moment, where discreteness of the dipole symmetry is enforced by periodic boundary conditions, with 𝐿 the system size. We show that in these systems a symmetric, gapped, and nondegenerate ground state requires not only integer charge filling, but also a fixed value of the dipole filling, while other fractional dipole fillings enforce either a gapless or symmetry-breaking ground state. In contrast with prior results in the literature, we find that the dipole filling constraint depends both on the charge filling as well as the system size, emphasizing the subtle interplay of dipole symmetry with boundary conditions. We support our results with numerical simulations and exact results.
Copyright and License
© 2024 American Physical Society.
Acknowledgement
We are particularly grateful to John Sous for discussions at the beginning of this project. We also thank Pranay Gorantla, Jonah Herzog-Arbeitman, Michael Knap, Naren Manjunath, Nati Seiberg, and Sahand Seifnashri for stimulating discussions and feedback.
Funding
This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics under Award No. DE-SC0009988 (A.P.) and by the NSF under Grant No. DMR 1928166 (F.J.B.). A.P. thanks the KITP, which is supported by the National Science Foundation under Grant No. NSF PHY-1748958, for its hospitality during the “Topology, Symmetry, and Interactions in Crystals” program, when part of this work was completed. This work was also supported by the Walter Burke Institute for Theoretical Physics at Caltech and the Institute for Quantum Information and Matter (S.M.). S.M. also acknowledges the hospitality of the Center for Quantum Phenomena (CQP) at NYU, the Aspen Center for Physics (ACP), and NORDITA Stockholm, where parts of this work were completed. ACP is supported by National Science Foundation Grants No. PHY-1607611 and No. PHY-2210452.
Supplemental Material
See Supplemental Material for details on the origin dependence of the dipole filling constraint, the minimal coupling procedure, results for fermionic and half-integer spin systems, the continuum limit, and analytic results based on exact mappings and matrix product states.
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Additional details
- United States Department of Energy
- DE-SC0009988
- National Science Foundation
- DMR-1928166
- National Science Foundation
- PHY-1748958
- California Institute of Technology
- National Science Foundation
- PHY-1607611
- National Science Foundation
- PHY-2210452
- Accepted
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2024-09-09Accepted
- Caltech groups
- Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
- Publication Status
- Published