Related papers: HofstadterTools: A Python package for analyzing th…
We construct generalized Hofstadter models that possess "color-entangled" flat bands and study interacting many-body states in such bands. For a system with periodic boundary conditions and appropriate interactions, there exist gapped…
Spinless, interacting electrons on a finite size triangular lattice moving in an extremely strong perpendicular magnetic field are studied and compared with the results on a square lattice. Using a Falicov-Kimball model, the effects of the…
Complete characterization of states and processes that occur within quantum devices is crucial for understanding and testing their potential to outperform classical technologies for communications and computing. However, solving this task…
We theoretically introduce and study a three-dimensional Hofstadter model with linearly varying non-Abelian gauge potentials along all three dimensions. The model can be interpreted as spin-orbit coupling among a trio of Hofstadter…
Statistical physics models ranging from simple lattice to complex quantum Hamiltonians are one of the mainstays of modern physics, that have allowed both decades of scientific discovery and provided a universal framework to understand a…
The trans-series completion of perturbative series of a wide class of quantum mechanical systems can be determined by combining the resurgence program and extra input coming from exact WKB analysis. In this paper, we reexamine the…
Two-dimensional lattice models subjected to an external effective magnetic field can form nontrivial band topologies characterized by nonzero integer band Chern numbers. In this Letter, we investigate such a lattice model originating from…
We present PYATB, a Python package designed for computing band structures and related properties of materials using the ab initio tight-binding Hamiltonian. The Hamiltonian is directly obtained after conducting self-consistent calculations…
Multiscale modeling, which integrates material properties from ab initio calculations into continuum-scale simulations, is a promising strategy for optimizing semiconductor devices. However, a key challenge remains: while ab initio methods…
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…
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…
When subjected to a strong magnetic field, electrons on a two-dimensional lattice acquire a fractal energy spectrum called Hofstadter's butterfly. In addition to its unique recursive structure, the Hofstadter butterfly is intimately linked…
Certain aspects of some unitary quantum systems are well-described by evolution via a non-Hermitian effective Hamiltonian, as in the Wigner-Weisskopf theory for spontaneous decay. Conversely, any non-Hermitian Hamiltonian evolution can be…
We revisit the Hofstadter butterfly for a subset of topologically trivial Bloch bands arising from a continuum free electron Hamiltonian in a periodic lattice potential. We employ the recently developed procedure -- which was previously…
In this paper, we present a Hopf algebra description of a bosonic quantum model, using the elementary combinatorial elements of Bell and Stirling numbers. Our objective in doing this is as follows. Recent studies have revealed that…
We explore a technique for probing energy spectra in synthetic lattices that is analogous to scanning tunneling microscopy. Using one-dimensional synthetic lattices of coupled atomic momentum states, we explore this spectroscopic technique…
Recent advances in realizing artificial gauge fields on optical lattices promise experimental detection of topologically non-trivial energy spectra. Self-similar fractal energy structures generally known as Hofstadter butterflies depend…
We point out that the recent conjectural solution to the spectral problem for the Hamiltonian $H=e^{x}+e^{-x}+e^{p}+e^{-p}$ in terms of the refined topological invariants of a local Calabi-Yau geometry has an intimate relation with…
The manipulation of the quantum states of light in linear optical systems has multiple applications in quantum optics and quantum computation. The package QOptCraft gives a collection of methods to solve some of the most usual problems when…
The Hofstadter butterfly is one of the first and most fascinating examples of the fractal and self-similar quantum nature of free electrons in a lattice pierced by a perpendicular magnetic field. However, the direct experimental…