Characterizing $S=3/2$ AKLT Hamiltonian with Scanning Tunneling Spectroscopy
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866929745446305792 |
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| author | Ferri-Cortés, M. Henriques, J. C. G. Fernández-Rossier, J. |
| author_facet | Ferri-Cortés, M. Henriques, J. C. G. Fernández-Rossier, J. |
| contents | The AKLT Hamiltonian is a particular instance of a general class of model Hamiltonians defined in lattices with coordination $z$ where each site hosts a spins $S=z/2$, interacting both with linear and non-linear exchange couplings. In two dimensions, the AKLT model features a gap in the spectrum, and its ground state is a valence bond solid state; that is an universal resource for measurement based quantum computing, motivating the quest of physical systems that realize this Hamiltonian. Given a finite-size system described with a specific instance of this general class of models, we address the question of how to asses if such system is a realization of the AKLT model using inelastic tunnel spectroscopy implemented with scanning tunnel microscopy (IETS-STM). We propose two approaches. First, in the case of a dimer, we show how to leverage non-equilibrium IETS-STM to obtain the energies of all excited states, and determine thereby the magnitude of both linear and non-linear exchange interactions. Second, we explore how IETS can probe the in-gap excitations associated to edge spins. In the AKLT limit, spins $S=3/2$ at the edge of the lattice have coordination 2, giving rise to $S=1/2$ dangling spins that can be probed with IETS. We propose a $S=1/2$ effective Hamiltonian to describe the interactions between these dangling spins in the neighborhood of the AKLT point, where their degeneracy lifted. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_04676 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Characterizing $S=3/2$ AKLT Hamiltonian with Scanning Tunneling Spectroscopy Ferri-Cortés, M. Henriques, J. C. G. Fernández-Rossier, J. Mesoscale and Nanoscale Physics The AKLT Hamiltonian is a particular instance of a general class of model Hamiltonians defined in lattices with coordination $z$ where each site hosts a spins $S=z/2$, interacting both with linear and non-linear exchange couplings. In two dimensions, the AKLT model features a gap in the spectrum, and its ground state is a valence bond solid state; that is an universal resource for measurement based quantum computing, motivating the quest of physical systems that realize this Hamiltonian. Given a finite-size system described with a specific instance of this general class of models, we address the question of how to asses if such system is a realization of the AKLT model using inelastic tunnel spectroscopy implemented with scanning tunnel microscopy (IETS-STM). We propose two approaches. First, in the case of a dimer, we show how to leverage non-equilibrium IETS-STM to obtain the energies of all excited states, and determine thereby the magnitude of both linear and non-linear exchange interactions. Second, we explore how IETS can probe the in-gap excitations associated to edge spins. In the AKLT limit, spins $S=3/2$ at the edge of the lattice have coordination 2, giving rise to $S=1/2$ dangling spins that can be probed with IETS. We propose a $S=1/2$ effective Hamiltonian to describe the interactions between these dangling spins in the neighborhood of the AKLT point, where their degeneracy lifted. |
| title | Characterizing $S=3/2$ AKLT Hamiltonian with Scanning Tunneling Spectroscopy |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2503.04676 |