Related papers: Thermal Hofstadter Butterflies
We investigate the dynamics of neutral atoms in a 2D optical lattice which traps two distinct internal states of the atoms in different columns. Two Raman lasers are used to coherently transfer atoms from one internal state to the other,…
The Hofstadter butterfly is a quantum fractal with a highly complex nested set of gaps, where each gap represents a quantum Hall state whose quantized conductivity is characterized by topological invariants known as the Chern numbers. Here…
Statistical mechanics is founded on the assumption that a system can reach thermal equilibrium, regardless of the starting state. Interactions between particles facilitate thermalization, but, can interacting systems always equilibrate…
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 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 finite temperature properties of two-component fermionic atoms trapped in a two-dimensional optical lattice. We apply the self-energy functional approach to the two-dimensional Hubbard model with a harmonic trapping potential,…
Electrons on a two-dimensional (2$d$) lattice which is exposed to a strong uniform magnetic field show intriguing physical phenomena. The spectrum of such systems exhibits a complex (multi-)band structure known as Hofstadter's butterfly.…
We study thermodynamic properties of the two-dimensional (2D) Falicov-Kimball model in the presence of external magnetic field perpendicular to the lattice. The field is taken into account by the Peierls substitution in the hopping term. In…
Hofstadter's diagram, or the energy spectrum against the magnetic field in tight-binding systems, is obtained for the models having flat (dispersionless) one-electron band(s) that have originally been proposed for itinerant spin…
The Hofstadter model illustrates the notion of topological quantum numbers and how they account for the quantization of the Hall conductance. It gives rise to colorful fractal diagrams of butterflies where the colors represent the…
Despite the multi-band spectrum of the widely-known Hofstadter butterfly, it turns out that the pairing correlations of the time-reversal-symmetric Hofstadter-Hubbard model are well-described by a single order parameter that is uniform in…
Transition metal dichalcogenide moir\'e homobilayers have emerged as a platform in which magnetism, strong correlations, and topology are intertwined. In a large magnetic field, the energetic alignment of states with different spin in these…
This is a short review of the recent progresses on Hofstadter butterfly in graphene, organized in the following. We first briefly introduce the Hofstadter butterfly, including the theoretic toy model of Bloch electrons in the magnetic…
We present a new simple and easy-to-implement one-dimensional phononic system whose spectrum exactly corresponds to the Hofstadter butterfly when a parameter is modulated. The system consists of masses that are coupled by linear springs and…
We have studied the revival of Hofstadter butterfly due to the competition between disorder and electronic interaction using mean field approximation of unrestricted Hartree Fock method at zero temperature for two dimensional square and…
In this chapter, we investigate the energy spectra as well as the bulk and surface states in a two-dimensional system composed of a coupled stack of one-dimensional dimerized chains in the presence of an external magnetic field.…
Two-dimensional (2D) periodic electric modulations of a 2D electron gas split each Landau level into the well-known butterfly-type spectrum described by a Harper-type equation multiplied by an envelope function. This equation is slightly…
We calculate several thermodynamic quantities for repulsively interacting one-dimensional fermions.We solve the Hubbard model at both zero and finite temperatures using the Bethe-ansatz method. For arbitrary values of the chemical…
Spinless fermions on highly frustrated lattices are characterized by a lowest single-particle band which is completely flat. Concrete realizations are provided by the sawtooth chain and the kagome lattice. For these models a real-space…
We develop a theory of photoluminescence using a time-dependent Hartree-Fock approximation that is appropriate for the two-dimensional Wigner crystal in a strong magnetic field. The cases of localized and itinerant holes are both studied.…