Extracting the number of type-B Goldstone modes and the dynamical critical exponent for a type of scale-invariant states

Huan-Qiang Zhou; Yan-Wei Dai; Qian-Qian Shi; Ian P. McCulloch; Murray T. Batchelor

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arXiv · 2309.04953

Extracting the number of type-B Goldstone modes and the dynamical critical exponent for a type of scale-invariant states

Huan-Qiang Zhou·Yan-Wei Dai·Qian-Qian Shi·Ian P. McCulloch·Murray T. Batchelor

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Abstract

A generic scheme is proposed to perform a finite-entanglement scaling analysis for scale-invariant states, which appear to be highly degenerate ground states arising from spontaneous symmetry breaking with type-B Goldstone modes. This allows us to extract the number of type-B Goldstone modes and the dynamical critical exponent, in combination with a finite block-size scaling analysis, from numerical simulations of quantum many-body systems in the context of tensor network representations. The number of type-B Goldstone modes is identical to the fractal dimension, thus reflecting an abstract fractal underlying the ground state subspace. As illustrative examples, we investigate the spin-$s$ Heisenberg ferromagnetic model, the $\rm{SU}(3)$ ferromagnetic model and the $\rm{SO}(4)$ spin-orbital model.

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Huan-Qiang Zhou, Yan-Wei Dai, Qian-Qian Shi, Ian P. McCulloch, Murray T. Batchelor. 2023-11-30. Extracting the number of type-B Goldstone modes and the dynamical critical exponent for a type of scale-invariant states. https://arxiv.org/abs/2309.04953

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