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arXiv · 2412.15724

Entanglement entropy for the one-dimensional flat-band ferromagnetic Tasaki model: spontaneous symmetry breaking with one type-B Goldstone mode

Huan-Qiang Zhou·Qian-Qian Shi·Ian P. McCulloch·J. O. Fjærestad
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Abstract

The one-dimensional flat-band ferromagnetic Tasaki model exhibits spontaneous symmetry breaking from ${\rm SU}(2)$ to ${\rm U}(1)$ with one type-B Goldstone mode, featuring that the highest weight state is entangled at quarter filling, but there is always a choice to keep the highest weight state unentangled away from quarter filling. It is found that the ground-state degeneracies under both periodic and open boundary conditions constitute essentially the Fibonacci sequences, behaving asymptotically as the golden spiral - a self-similar geometric object. A set of orthonormal basis states are generated from the repeated action of the lowering operator of the symmetry group ${\rm SU}(2)$ on the highest weight state at a specific filling. In particular, it is possible to construct the orthonormal basis states reflecting an abstract fractal underlying the ground-state subspace, which are permutation-invariant away from quarter filling, but not at quarter filling. As a consequence, there exists a singularity that accounts for the emergence of the saturated flat-band ferromagnetism at quarter filling. We perform a systematic finite system-size scaling analysis of the entanglement entropy, thus confirming that it scales logarithmically with the block size in the thermodynamic limit, with the prefactor being half the number of type-B Goldstone modes, for the orthonormal basis states at and away from quarter filling.

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Huan-Qiang Zhou, Qian-Qian Shi, Ian P. McCulloch, J. O. Fjærestad. 2024-12-20. Entanglement entropy for the one-dimensional flat-band ferromagnetic Tasaki model: spontaneous symmetry breaking with one type-B Goldstone mode. https://arxiv.org/abs/2412.15724

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