Related papers: Butterflies and topological quantum numbers
The Hopfield model in a transverse field is investigated in order to clarify how quantum fluctuations affect the macroscopic behavior of neural networks. Using the Trotter decomposition and the replica method, we find that the $\alpha$ (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…
With the idea of an eventual classification of 3-bridge links,\ we define a very nice class of 3-balls (called butterflies) with faces identified by pairs, such that the identification space is $S^{3},$ and the image of a prefered set of…
Formulation of quantum Hall dynamics using von Neumann lattice of guiding center coordinates is presented. A topological invariant expression of the Hall conductance is given and a new mean field theory of the fractional Hall effect based…
Crystalline symmetries give rise to topological invariants that can distinguish quantum phases of matter. Understanding these in strongly interacting systems is an ongoing research direction requiring non-perturbative methods. Recent…
We consider a holographic description of a system of strongly coupled fermions in 2+1 dimensions based on a D7-brane probe in the background of D3-branes, and construct stable embeddings by turning on worldvolume fluxes. We study the system…
We investigate the effect that density-wave states have on the Hofstadter Butterfly. We first review the problem of the $d$-density wave on a square lattice and then numerically solve the $d$-density wave problem when an external magnetic…
Canonical BRST quantization of the topological particle defined by a Morse function h is described. Stochastic calculus, using Brownian paths which implement the WKB method in a new way providing rigorous tunnelling results even in curved…
The conductance of a two-dimensional electron gas at the transition from one quantum Hall plateau to the next has sample-specific fluctuations as a function of magnetic field and Fermi energy. Here we identify a universal feature of these…
We study a class of discrete-time quantum walks with inhomogeneous coins defined in [Y. Shikano and H. Katsura, Phys. Rev. E {\bf 82}, 031122 (2010)]. We establish symmetry properties of the spectrum of the evolution operator, which…
A topological phase can be engineered in quantum physics from the Bloch sphere of a spin-1/2 showing an hedgehog structure as a result of a radial magnetic field. We elaborate on a relation between the formation of an entangled wavefunction…
It is shown that the set of optical quantum tomograms can be provided with the topology of Frechet space. In such a case the conjugate space will consist of symbols of quantum observables including all polynomials of the position and…
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 investigate the fractional energy spectrum and quantum Hall response of a two-dimensional 1/5-depleted square lattice subjected to a perpendicular magnetic field. Using a tight-binding model that includes both nearest-neighbor (t_1) and…
The relativistic two-particle quantum mixtures are studied from the topological point of view. The mixture field variables can be transformed in such a way that a kinematical decoupling of both particle degrees of freedom takes place with a…
Phenomena associated with topological properties of physical systems are naturally robust against perturbations. This robustness is exemplified by quantized conductance and edge state transport in the quantum Hall and quantum spin Hall…
We calculate a topological invariant, whose value would coincide with the Chern number in case of integer quantum Hall effect, for fractional quantum Hall states. In case of Abelian fractional quantum Hall states, this invariant is shown to…
We investigate the electronic properties in the Bloch electron on a square lattice with vacancies in the uniform magnetic field. We show that a single vacancy site introduced to the system creates a defect energy level in every single…
We study torsors over 2-groups and their morphisms. In particular, we study the first non-abelian cohomology group with values in a 2-group. Butterfly diagrams encode morphisms of 2-groups and we employ them to examine the functorial…
The recent discoveries about topological insulators have been promoting theoretical and experimental research. In this dissertation, the basic concepts of topological insulators and the Quantum Hall Effect are reviewed focusing the…