Related papers: Fractality of Hofstadter Butterfly in Specific Hea…
Motivated by recent realizations of two-dimensional (2D) superconducting-qubit lattices, we propose a protocol to simulate Hofstadter butterfly with synthetic gauge fields in superconducting circuits. Based on the existing 2D…
We revisit the problem of self-similar properties of the Hofstadter butterfly spectrum, focusing on spectral as well as topological characteristics. In our studies involving any value of magnetic flux and arbitrary flux interval, we single…
Topological description of hierarchical sets of spectral gaps of Hofstadter butterfly is found to be encoded in a quasicrystal where magnetic flux plays the role of a phase factor that shifts the origin of the quasiperiodic order. Revealing…
We address the energy spectrum of honeycomb lattice with various defects or impurities under a perpendicular magnetic field. We use a tight-binding Hamiltonian including interactions with the nearest neighbors and investigate its energy…
Gauge potentials with different configurations have been recently realized in the optical lattice experiments. It is remarkable that one of the simplest gauge can generate particle energy spectrum with the self-similar structure known as a…
We study Hofstadter bilayers, i.e. coupled hopping models on two-dimensional square lattices in a perpendicular magnetic field. Upon tracing out one of the layers, we find an explicit expression for the resulting entanglement spectrum in…
A system presenting fractal structure in its thermodynamical functions is introduced, and it is shown that Tsallis statistics is the correct framework for describing the thermodynamical aspects of such fractal. Its Haussdorf dimension and…
Motivated by recent experimental attempts to detect the Hofstadter butterfly, we numerically calculate the Hall conductivity in a modulated two-dimensional electron system with disorder in the quantum Hall regime. We identify the critical…
We consider a thermal quantum harmonic oscillator weakly coupled to a heat bath at a different temperature. We analytically study the quantum heat exchange statistics between the two systems using the quantum-optical master equation. We…
We study an energy spectrum of electron moving under the constant magnetic field in two dimensional noncommutative space. It take place with the gauge invariant way. The Hofstadter butterfly diagram of the noncommutative space is calculated…
The self-similar energy spectrum of a particle in a periodic potential under a magnetic field, known as the Hofstadter butterfly, is determined by the lattice geometry as well as the external field. Recent realizations of artificial gauge…
The scattering properties of quantum particles on fractal potentials at different stages of fractal growth are obtained by means of the transfer matrix method. This approach can be easily adopted for project assignments in introductory…
Electrons moving through a spatially periodic lattice potential develop a quantized energy spectrum consisting of discrete Bloch bands. In two dimensions, electrons moving through a magnetic field also develop a quantized energy spectrum,…
The Aubry-Andre model is a one-dimensional lattice model for quasicrystals with localized and delocalized phases. At the localization transition point, the system displays fractal spectrum, which relates to the Hofstadter butterfly. In this…
We study the effect of interactions on the Hofstadter butterfly of the honeycomb lattice. We show that the interactions induce charge ordering that breaks the translational and rotational symmetries of the system. These phase transitions…
Electrons on the lattice subject to a strong magnetic field exhibit the fractal spectrum of electrons, which is known as the Hofstadter butterfly. In this work, we investigate unconventional superconductivity in a three-dimensional…
The first quantum fractal discovered in physics is the Hofstadter butterfly. It stems from large external magnetic fields. We discover instead a new class of non-Hermitian quantum fractals (NHQFs) emerging in coupled Hatano-Nelson models on…
The evaluation of the specific heat of an open, damped quantum system is a subtle issue. One possible route is based on the thermodynamic partition function which is the ratio of the partition functions of system plus bath and of the bath…
We give a perspective on the Hofstadter butterfly (fractal energy spectrum in magnetic fields), which we have shown to arise specifically in three-dimensional(3D) systems in our previous work. (i) We first obtain the `phase diagram' on a…
For a three-dimensional lattice in magnetic fields we have shown that the hopping along the third direction, which normally tends to smear out the Landau quantization gaps, can rather give rise to a fractal energy spectram akin to…