Caution on emergent continuous symmetry: a Monte Carlo investigation of transverse-field frustrated Ising model on triangle and honeycomb lattices

Abstract

Continuous symmetries are believed to emerge at many quantum critical points in frustrated magnets. In this work, we study two candidates of this paradigm: the transverse-field frustrated Ising model (TFFIM) on the triangle and the honeycomb lattices. The former is the prototypical example of this paradigm, and the latter has recently been proposed as another realization. Our large-scale Monte Carlo simulation confirms that the quantum phase transition (QPT) in the triangle lattice TFFIM indeed hosts an emergent O(2) symmetry, but that in the honeycomb lattice TFFIM is a first-order QPT and does not have an emergent continuous symmetry. Furthermore, our analysis of the order parameter histogram reveals that such different behavior originates from the irrelevance and relevance of anisotropic terms near the QPT in the low-energy effective theory of the two models. The comparison between theoretical analysis and numerical simulation in this work paves the way for scrutinizing investigation of emergent continuous symmetry at classical and quantum phase transitions.

9 pages, 8 figures, update figs and references

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• Itinerant Quantum Critical Point with Fermion Pockets and Hot Spots
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• Intrinsic quantum Ising model on a triangular lattice magnet TmMgGaO${}_4$ and beyond
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• Phase Diagram of Triangular Lattice Quantum Ising Model under External Field
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• Simulating the Transverse Field Ising Model on the Kagome Lattice using a Programmable Quantum Annealer
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• Emergent transverse-field Ising model in ${\mathbf{d}}^4$ spin-orbit Mott insulators
• Symmetrizing the Constraints -- Density Matrix Renormalization Group for Constrained Lattice Models
• Ultrafast light-induced long range antiferromagnetic correlations in paramagnets
• Extracting quantum-critical properties from directly evaluated enhanced perturbative continuous unitary transformations