Probing the Hofstadter butterfly with the quantum oscillation of magnetization

TL;DR

This paper introduces a novel quantum transfer matrix method to accurately analyze the thermodynamic properties of the Hofstadter model, revealing the fractal energy spectrum through magnetization oscillations.

Contribution

A new quantum transfer matrix approach enables finite-temperature analysis of the Hofstadter model's thermodynamics, overcoming previous computational limitations.

Findings

Quantum correction to dHvA oscillation reflects Hofstadter butterfly energy structure

Method allows calculation in the thermodynamic limit at finite temperatures

Potential experimental detection via superlattice or cold atom systems

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.