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Unlocking the potential of topological order in many-body spin systems has been a key goal in quantum materials research. Despite extensive efforts, the quest for a versatile platform enabling site-selective spin manipulation, essential for tuning and probing diverse topological phases, has persisted. Here we utilize on-surface synthesis to construct spin-1/2 alternating-exchange Heisenberg chains by covalently linking Clar's goblets-nanographenes each hosting two antiferromagnetically coupled spins. Using scanning tunnelling microscopy, we exert atomic-scale control over chain lengths, parities and exchange-coupling terminations, and probe their magnetic response via inelastic tunnelling spectroscopy. Our investigation confirms the gapped nature of bulk excitations in the chains, known as triplons. Their dispersion relation is extracted from the spatial variation of tunnelling spectral amplitudes. Depending on the parity and termination of chains, we observe varying numbers of in-gap spin-1/2 edge excitations, reflecting the degeneracy of distinct topological ground states in the thermodynamic limit. By monitoring interactions between these edge spins, we identify the exponential decay of spin correlations. Our findings present a phase-controlled many-body platform, opening avenues toward spin-based quantum devices.
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http://dx.doi.org/10.1038/s41565-024-01805-z | DOI Listing |
Phys Rev Lett
August 2025
Indian Institute of Science, Centre for Condensed Matter Theory, Department of Physics, Bengaluru 560 012, India.
We present a detailed analytical and numerical examination, on square and triangular lattices, of the nonreciprocal planar spin model introduced in Dadhichi et al. [Phys. Rev.
View Article and Find Full Text PDFPhys Rev Lett
August 2025
Weizmann Institute of Science, Department of Physics of Complex Systems, Rehovot 761001, Israel.
The coupling of lasers plays an important role in a variety of research activities, from generating high-power lasers to investigating out-of-equilibrium coupled systems. This Letter presents our investigations of Hermitian coupling in arrays of lasers, where it is possible to control both the amplitude and phase of the coupling and generate artificial gauge fields. The Hermitian coupling is demonstrated in three laser array geometries: a square array of 100 lasers with controlled laser coupling for obtaining continuous control over the phase-locked state, a triangular array of 130 lasers with controlled chirality of the lasers, and a ring array of eight lasers with a controlled topological charge.
View Article and Find Full Text PDFPhys Rev Lett
August 2025
Weizmann Institute of Science, Department of Condensed Matter Physics, Rehovot 7610001, Israel.
We address the problem of identifying a 2+1D topologically ordered phase using measurements on the ground-state wave function. For nonchiral topological order, we describe a series of bulk multipartite entanglement measures that extract the invariants ∑_{a} d_{a}^{2}θ_{a}^{r} for any r≥2, where d_{a} and θ_{a} are the quantum dimension and topological spin of an anyon a, respectively. These invariants are obtained as expectation values of permutation operators between 2r replicas of the wave function, applying different permutations on four distinct regions of the plane.
View Article and Find Full Text PDFPhys Rev Lett
August 2025
Laboratoire de Physique Théorique de la Matière Condensée, Sorbonne Université, CNRS, 75005 Paris, France.
We investigate nonreciprocal XY (NRXY) models defined on two-dimensional lattices in which the coupling strength of a spin with its neighbors varies with their position in the frame defined by the current spin orientation. As expected from the seminal work of Dadhichi et al., [Nonmutual torques and the unimportance of motility for long-range order in two-dimensional flocks, Phys.
View Article and Find Full Text PDFChaos
September 2025
Emergent Photonics Research Centre, Department of Physics, Loughborough University, LE11 3TU Loughborough, United Kingdom.
Photonic Reservoir Computing (RC) systems leverage the complex propagation and nonlinear interaction of optical waves to perform information processing tasks. These systems employ a combination of optical data encoding (in the field amplitude and/or phase), random scattering, and nonlinear detection to generate nonlinear features that can be processed via a linear readout layer. In this work, we propose a novel scattering-assisted photonic reservoir encoding scheme where the input phase is deliberately wrapped multiple times beyond the natural period of the optical waves [0,2π).
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