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Abstract The interplay of correlated spatial modulation and symmetry breaking leads to quantum critical phenomena intermediate between those of the clean and randomly disordered cases. By performing a detailed analytic and numerical case study of the quasi-periodically (QP) modulated transverse field Ising chain, we provide evidence for the conjectures of reference (Crowleyet al2018Phys. Rev. Lett.120175702) regarding the QP-Ising universality class. In the generic case, we confirm that the logarithmic wandering coefficientwgoverns both the macroscopic critical exponents and the energy-dependent localisation length of the critical excitations. However, for special values of the phase difference Δ between the exchange and transverse field couplings, the QP-Ising transition has different properties. For Δ = 0, a generalised Aubry–André duality prevents the finite energy excitations from localising despite the presence of logarithmic wandering. For Δ such that the fields and couplings are related by a lattice shift, the wandering coefficientwvanishes. Nonetheless, the presence of small couplings leads to non-trivial exponents and localised excitations. Our results add to the rich menagerie of quantum Ising transitions in the presence of spatial modulation.
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This content will become publicly available on April 25, 2026
Observation of generalized t-J spin dynamics with tunable dipolar interactions
Long-range and anisotropic dipolar interactions profoundly modify the dynamics of particles hopping in a periodic lattice potential. We report the realization of a generalizedt-Jmodel with dipolar interactions using a system of ultracold fermionic molecules with spin encoded in the two lowest rotational states. We independently tuned the dipolar Ising and spin-exchange couplings and the molecular motion and studied their interplay on coherent spin dynamics. Using Ramsey spectroscopy, we observed and modeled interaction-driven contrast decay that depends strongly both on the strength of the anisotropy between Ising and spin-exchange couplings and on motion. This study paves the way for future exploration of kinetic spin dynamics and quantum magnetism with highly tunable molecular platforms in regimes that are challenging for existing numerical and analytical methods.
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- PAR ID:
- 10592870
- Publisher / Repository:
- Science
- Date Published:
- Journal Name:
- Science
- Volume:
- 388
- Issue:
- 6745
- ISSN:
- 0036-8075
- Page Range / eLocation ID:
- 381 to 386
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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