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

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arxiv 2310.19880 v2 pith:N7KJKFVS submitted 2023-10-30 cond-mat.str-el cond-mat.stat-mechhep-lathep-th

Johannes S. Hofmann , Florian Goth , Wei Zhu , Yin-Chen He , Emilie Huffman This is my paper
classification cond-mat.str-elcond-mat.stat-mechhep-lathep-th
keywords fuzzyquantumspheretransitioncarloisingmodelmonte
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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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Cited by 3 Pith papers

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  1. Chern-Simons-matter conformal field theory on fuzzy sphere: Confinement transition of Kalmeyer-Laughlin chiral spin liquid

    cond-mat.str-el 2025-07 conditional novelty 8.0 of 10

    A fuzzy-sphere exact diagonalization study shows the fIQH to bFQH transition is continuous, with emergent conformal symmetry and a single relevant singlet of scaling dimension Delta_S = 1.52(18).

  2. 3d Conformal Field Theories via Fuzzy Sphere Algebra

    cond-mat.str-el 2026-02 conditional novelty 6.0 of 10

    The fuzzy-sphere density-mode algebra is a genuine Lie algebra, but a direct density-mode realization of the 3d conformal algebra so(3,2) exists only for the two-electron system.

  3. The $O(N)$ Free-Scalar and Wilson-Fisher Conformal Field Theories on the Fuzzy Sphere

    cond-mat.str-el 2025-12 conditional novelty 5.0 of 10

    Fuzzy-sphere Hamiltonians realize the O(2), O(3) and O(4) Wilson-Fisher and free-scalar CFTs numerically, with spectra and correlators matching conformal bootstrap expectations.

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