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arXiv · 1711.11401

Tensor-network study of quantum phase transition on Sierpiński fractal

Roman Krcmar·Jozef Genzor·Yoju Lee·Hana Čenčariková·Tomotoshi Nishino·Andrej Gendiar
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Abstract

The transverse-field Ising model on the Sierpiński fractal, which is characterized by the fractal dimension $\log_2^{~} 3 \approx 1.585$, is studied by a tensor-network method, the Higher-Order Tensor Renormalization Group. We analyze the ground-state energy and the spontaneous magnetization in the thermodynamic limit. The system exhibits the second-order phase transition at the critical transverse field $h_{\rm c}^{~} = 1.865$. The critical exponents $β\approx 0.198$ and $δ\approx 8.7$ are obtained. Complementary to the tensor-network method, we make use of the real-space renormalization group and improved mean-field approximations for comparison.

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Roman Krcmar, Jozef Genzor, Yoju Lee, Hana Čenčariková, Tomotoshi Nishino, Andrej Gendiar. 2018-11-09. Tensor-network study of quantum phase transition on Sierpiński fractal. https://doi.org/10.1103/physreve.98.062114

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