Probing the Hofstadter butterfly with the quantum oscillation of magnetization

Abstract

We have developed a different quantum transfer matrix method to accurately determine thermodynamic properties of the Hofstadter model. This method resolves a technical problem which is intractable by other methods and makes the calculation of physical quantities of the Hofstadter model in the thermodynamic limit at finite temperatures feasible. It is shown that the quantum correction to the de Haas-van Alphen (dHvA) oscillation of magnetization bears the energy structure of Hofstadter butterfly. The measurement of this quantum correction, which can be materialized on the superlattice or cold atom systems, can reveal unambiguously the Hofstadter fractal energy spectrum.

4 pages, 2 figures

References in corpus (2)

• Trapped Fermi Gases in Rotating Optical Lattices: Realization and Detection of the Topological Hofstadter Insulator
• Semiclassical analysis and the magnetization of the Hofstadter model

Cited by in corpus (5)

• Quantum oscillations of magnetization in the tight-binding electrons on honeycomb lattice
• Seeing Hofstadter's Butterfly in Atomic Fermi Gases
• Quantum transfer matrix method for one-dimensional disordered electronic systems
• Fractality of Hofstadter Butterfly in Specific Heat Oscillation
• Anomalous Landau levels and quantum oscillation in rotation-invariant insulators