Related papers: Non-Hermitian Quantum Fractals
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,…
We study the non-Hermitian Hofstadter dynamics of a quantum particle with biased motion on a square lattice in the background of a magnetic field. We show that in quasi-momentum space the energy spectrum is an overlap of infinitely many…
This paper unveils a mapping between a quantum fractal that describes a physical phenomena, and an abstract geometrical fractal. The quantum fractal is the Hofstadter butterfly discovered in 1976 in an iconic condensed matter problem of…
Self-similarity and fractals have fascinated researchers across various disciplines. In graphene placed on boron nitride and subjected to a magnetic field, self-similarity appears in the form of numerous replicas of the original Dirac…
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…
Hofstadter showed that the energy levels of electrons on a lattice plotted as a function of magnetic field form an beautiful structure now referred to as "Hofstadter's butterfly". We study a non-Hermitian continuation of Hofstadter's model;…
The \lq Hofstadter butterfly', a plot of the spectrum of an electron in a two-dimensional periodic potential with a uniform magnetic field, contains subsets which resemble small, distorted images of the entire plot. We show how the sizes of…
Celebrating its golden jubilee, the Hofstadter butterfly fractal emerges as a remarkable fusion of art and science. This iconic X shaped fractal captivates physicists, mathematicians, and enthusiasts alike by elegantly illustrating the…
Real-to-complex spectral transitions and the associated spontaneous symmetry breaking of eigenstates are central to non-Hermitian physics, yet a comprehensive and universal theory that precisely describes the underlying physical mechanisms…
We show that constraints imposed by strong Hilbert space fragmentation (HSF) along with the presence of certain global symmetries can ensure the reality of eigenspectra of non-Hermitian quantum systems; such a reality cannot be guaranteed…
Fractals are ubiquitous in nature, and since Mandelbrot's seminal insight into their structure, there has been growing interest in them. While the topological properties of the limit sets of IFSs have been studied -- notably in the…
This paper investigates wave-packet dynamics in non-Hermitian lattice systems and reveals a surprising phenomenon: The simultaneous propagation of two distinct wavefronts, one traveling at the non-Hermitian velocity and the other at the…
The square-lattice quantum Heisenberg antiferromagnet displays a pronounced anomaly of unknown origin in its magnetic excitation spectrum. The anomaly manifests itself only for short wavelength excitations propagating along the direction…
Flat bands, in which kinetic energy is quenched and quantum states become macroscopically degenerate, host a rich variety of correlated and topological phases, from unconventional superconductors to fractional Chern insulators. In Hermitian…
We uncover the very rich graph topology of generic bounded non-Hermitian spectra, distinct from the topology of conventional band invariants and complex spectral winding. The graph configuration of complex spectra are characterized by the…
Quantum systems are often classified into Hermitian and non-Hermitian ones. Extraordinary non-Hermitian phenomena, ranging from the non-Hermitian skin effect to the supersensitivity to boundary conditions, have been widely explored. Whereas…
Non-Hermitian matrices are ubiquitous in the description of nature ranging from classical dissipative systems, including optical, electrical, and mechanical metamaterials, to scattering of waves and open quantum many-body systems. Seminal…
We give a simple toy model to study a famous Jahn-Teller type molecule. Finite lifetime due to non-adiabatic coupling and finite temperature effect results in the effective Hamiltonian to be non-Hermitian. This effect pulls a conical…
Non-Hermitian systems exhibit interesting band structures, where novel topological phenomena arise from the existence of exceptional points at which eigenvalues and eigenvectors coalesce. One important open question is how this would…
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…