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arXiv · 2310.19880

Quantum Monte Carlo Simulation of the 3D Ising Transition on the Fuzzy Sphere

Johannes S. Hofmann·Florian Goth·Wei Zhu·Yin-Chen He·Emilie Huffman
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Abstract

We present a numerical quantum Monte Carlo (QMC) method for simulating the 3D phase transition on the recently proposed fuzzy sphere [Phys. Rev. X 13, 021009 (2023)]. By introducing an additional $SU(2)$ layer degree of freedom, we reformulate the model into a form suitable for sign-problem-free QMC simulation. From the finite-size-scaling, we show that this QMC-friendly model undergoes a quantum phase transition belonging to the 3D Ising universality class, and at the critical point we compute the scaling dimensions from the state-operator correspondence, which largely agrees with the prediction from the conformal field theory. These results pave the way to construct sign-problem-free models for QMC simulations on the fuzzy sphere, which could advance the future study on more sophisticated criticalities.

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Johannes S. Hofmann, Florian Goth, Wei Zhu, Yin-Chen He, Emilie Huffman. 2023-10-30. Quantum Monte Carlo Simulation of the 3D Ising Transition on the Fuzzy Sphere. https://doi.org/10.21468/scipostphyscore.7.2.028

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