Filling constraints on translation invariant dipole conserving systems

Journal Article · 18 September 2024 · Physical Review. B

DOI: https://doi.org/10.1103/physrevb.110.l121113 · OSTI ID:2460504

Burnell, Fiona J. ^[1]; Moudgalya, Sanjay  ^[2]; Prem, Abhinav  ^[3]

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1. University of Minnesota, Minneapolis, MN (United States); Institute for Advanced Study
2. California Institute of Technology (CalTech), Pasadena, CA (United States); Technische Universität München (TUM), Garching (Germany); Munich Center for Quantum Science and Technology (MCQST) (Germany)
3. Institute for Advanced Study, Princeton, NJ (United States)

Systems with conserved dipole moment have drawn considerable interest in light of their realization in recent experiments on tilted optical lattices. Here, an important question for 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 Z_L 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 non-degenerate 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.

• Research Organization: Institute for Advanced Study, Princeton, NJ (United States)
• Sponsoring Organization: USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF)
• Grant/Contract Number: SC0009988
• OSTI ID: 2460504
• Journal Information: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 12 Vol. 110; ISSN 2469-9950
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English