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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2508.02468 |
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| _version_ | 1866914452537868288 |
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| author | Papoular, D. J. |
| author_facet | Papoular, D. J. |
| contents | We theoretically identify observable consequences of spatial and spin symmetries on the dynamics of a small XXZ quantum simulator. Our proposed protocol relies on the choice of suitable initial states, and involves the measurement scheme whose experimental implementation is the simplest. We analyze a system of $N=2n=6$ to $12$ particles, trapped in a planar geometry comprised of two rings which exhibits point group symmetry $D_{nh}$. The particles represent effective spins whose interaction is described by the XXZ or Heisenberg Hamiltonian. The system is prepared in an initial state which is sitewise-factorized and invariant under all spatial symmetries, it evolves for a given time, after which the $z$-components of all $N$ spins are measured. We show that symmetries dictate (i) the qualitative behaviour of the measurement probabilities as a function of the evolution time, and (ii) the number of measurement results with different probabilities. We highlight the role of a twofold rotation of all spins. We also demonstrate that, in larger systems, the collapse of the initial state may be observed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_02468 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Measured dynamics of an XXZ quantum simulator in a highly symmetrical double-ringed geometry Papoular, D. J. Quantum Physics We theoretically identify observable consequences of spatial and spin symmetries on the dynamics of a small XXZ quantum simulator. Our proposed protocol relies on the choice of suitable initial states, and involves the measurement scheme whose experimental implementation is the simplest. We analyze a system of $N=2n=6$ to $12$ particles, trapped in a planar geometry comprised of two rings which exhibits point group symmetry $D_{nh}$. The particles represent effective spins whose interaction is described by the XXZ or Heisenberg Hamiltonian. The system is prepared in an initial state which is sitewise-factorized and invariant under all spatial symmetries, it evolves for a given time, after which the $z$-components of all $N$ spins are measured. We show that symmetries dictate (i) the qualitative behaviour of the measurement probabilities as a function of the evolution time, and (ii) the number of measurement results with different probabilities. We highlight the role of a twofold rotation of all spins. We also demonstrate that, in larger systems, the collapse of the initial state may be observed. |
| title | Measured dynamics of an XXZ quantum simulator in a highly symmetrical double-ringed geometry |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2508.02468 |