Quantum critical behavior of the quantum Ising model on fractal lattices

Abstract

I study the properties of the quantum critical point of the transverse-field quantum Ising model on various fractal lattices such as the Sierpiński carpet, Sierpiński gasket, and Sierpiński tetrahedron. Using a continuous-time quantum Monte Carlo simulation method and the finite-size scaling analysis, I identify the quantum critical point and investigate its scaling properties. Among others, I calculate the dynamic critical exponent and find that it is greater than one for all three structures. The fact that it deviates from one is a direct consequence of the fractal structures not being integer-dimensional regular lattices. Other critical exponents are also calculated. The exponents are different from those of the classical critical point, and satisfy the quantum scaling relation, thus confirming that I have indeed found the quantum critical point. I find that the Sierpiński tetrahedron, of which the dimension is exactly two, belongs to a different universality class than that of the two-dimensional square lattice. I conclude that the critical exponents depend on more details of the structure than just the dimension and the symmetry.

References in corpus (6)

• Effective quantum spin systems with ion traps
• 25th-order high-temperature expansion results for three-dimensional Ising-like systems on the simple cubic lattice
• Critical properties of Ising model on Sierpinski fractals. A finite size scaling analysis approach
• Entanglement in the quantum Ising model
• Effect of Quantum Fluctuations in an Ising System on Small-World Networks
• Quantum Monte Carlo study of the transverse-field quantum Ising model on infinite-dimensional structures

Cited by in corpus (6)

• Anyons and Fractional Quantum Hall Effect in Fractal Dimensions
• Tensor-network study of quantum phase transition on Sierpiński fractal
• Multipartite entanglement, quantum coherence, and quantum criticality in triangular and Sierpiński fractal lattices
• Anomalous quantum transport in fractal lattices
• Many-body localization on finite generation fractal lattices
• Quantum phase transition of the transverse-field quantum Ising model on scale-free networks