Localization and multifractal properties of the long-range Kitaev chain in the presence of an Aubry-André-Harper modulation

Last update: Apr 17, 2022

Overview

Localization and multifractal properties of the long-range Kitaev chain in the presence of an Aubry-André-Harper modulation

By Joana Fraxanet, Utso Bhattacharya, Tobias Grass, Maciej Lewenstein and Alexandre Dauphin

Content

This repository contains the code for the paper "Localization and multifractal properties of the long-range Kitaev chain in the presence of an Aubry-André-Harper modulation".

Abstract

In the presence of quasiperiodic potentials, the celebrated Kitaev chain presents an intriguing phase diagram with ergodic, localized and and multifractal states. In this work, we generalize these results by studying the localization properties of the Aubry-André-Harper model in the presence of long-range hopping and superconducting pairing amplitudes. These amplitudes decay with power-law exponents. To this end, we review and compare a toolbox of global and local characterization methods in order to investigate different types of transitions between ergodic, localized and multifractal states. We report energy-dependent transitions from ergodic to multifractal states for pairing terms with a decay exponent smaller than one and energy-dependent transitions from ergodic to localized states with an intermediate multifractal region for a decay exponent larger than one. The size of the intermediate multifractal region depends not only on the value of the superconducting pairing term, but also on the energy band. The transitions are not described by a mobility edge, but instead we report hybridization of bands with different types of localization properties. This leads to coexisting multifractal regimes where fractal dimensions follow different distributions.

The notebook data.ipynb, you can find the code that creates the data for the figures of the paper.
The figures of the paper can be generated from figures.ipynb.

An awesome list of AI for art and design - resources, and popular datasets and how we may apply computer vision tasks to art and design.

Awesome AI for Art & Design An awesome list of AI for art and design - resources, and popular datasets and how we may apply computer vision tasks to a

20 Dec 21, 2022

Built with Python programming language and QT library and Guess the number in three easy, medium and hard rolls

guess-the-numbers Built with Python programming language and QT library and Guess the number in three easy, medium and hard rolls Number guessing game

5 Oct 9, 2021

password-generator Built with Python programming language and QT library and Guess the number in three easy, medium and hard rolls Password generator

3 Oct 9, 2021

Cirq is a Python library for writing, manipulating, and optimizing quantum circuits and running them against quantum computers and simulators

Cirq is a Python library for writing, manipulating, and optimizing quantum circuits and running them against quantum computers and simulators. Install

3.6k Jan 7, 2023

A simple script written using symbolic python that takes as input a desired metric and automatically calculates and outputs the Christoffel Pseudo-Tensor, Riemann Curvature Tensor, Ricci Tensor, Scalar Curvature and the Kretschmann Scalar

2 Nov 27, 2021

🔩 Like builtins, but boltons. 250+ constructs, recipes, and snippets which extend (and rely on nothing but) the Python standard library. Nothing like Michael Bolton.

Boltons boltons should be builtins. Boltons is a set of over 230 BSD-licensed, pure-Python utilities in the same spirit as — and yet conspicuously mis

6k Jan 6, 2023

A free and open-source chess improvement app that combines the power of Lichess and Anki.

Localization and multifractal properties of the long-range Kitaev chain in the presence of an Aubry-André-Harper modulation

Related tags

Overview

Localization and multifractal properties of the long-range Kitaev chain in the presence of an Aubry-André-Harper modulation

Content

Abstract

You might also like...

An awesome list of AI for art and design - resources, and popular datasets and how we may apply computer vision tasks to art and design.

Built with Python programming language and QT library and Guess the number in three easy, medium and hard rolls

Built with Python programming language and QT library and Guess the number in three easy, medium and hard rolls

Cirq is a Python library for writing, manipulating, and optimizing quantum circuits and running them against quantum computers and simulators

A simple script written using symbolic python that takes as input a desired metric and automatically calculates and outputs the Christoffel Pseudo-Tensor, Riemann Curvature Tensor, Ricci Tensor, Scalar Curvature and the Kretschmann Scalar

🔩 Like builtins, but boltons. 250+ constructs, recipes, and snippets which extend (and rely on nothing but) the Python standard library. Nothing like Michael Bolton.

A free and open-source chess improvement app that combines the power of Lichess and Anki.

HPomb Is Socail Engineering Tool , Used For Bombing , Spoofing and Anonymity Available For Linux And Android(Termux)

TickerRain is an open-source web app that stores and analysis Reddit posts in a transparent and semi-interactive manner.

Releases(v.1.0.0)

v.1.0.0(Jan 10, 2022)

v.1.0(Jan 10, 2022)

v.1.0.0-alpha(Jan 10, 2022)

Owner

Joana Fraxanet

Check bookings for TUM libraries.

A Linux program to create a Windows USB stick installer from a real Windows DVD or image.

Repositório para estudo do airflow

Airflow Operator for running Soda SQL scans

Here is my Senior Design Project that I implemented to graduate from Computer Engineering.

AlexaUsingPython - Alexa will pay attention to your order, as: Hello Alexa, play music, Hello Alexa

This python code will get requests from SET (The Stock Exchange of Thailand) a previously-close stock price and return it in Thai Baht currency using beautiful soup 4 HTML scrapper.

An esoteric programming language that supports concurrency, regex, and web requests.

A simple but complete exercise to learning Python

Got-book-6 - LSTM trained on the first five ASOIAF/GOT books

Gba-free-fonts - Free font resources for GBA game development

プレヤフHackUチーム「キャット・タン」が作成したアプリ「illustection」

Just imagine normal bancho, but you can have multiple profiles and funorange speed up maps ranked

Experiments with Tox plugin system

A docker container (Docker Desktop) for a simple python Web app few unit tested

An example module hooking system, will be used in PySAMP.

A little tool that uses LLVM to extract simple "what does this do" level instruction information from all architectures.

Pipenv-local-deps-repro - Reproduction of a local transitive dependency on pipenv

Minterpy - Multidimensional interpolation in Python.

Code for ML, domain generation, graph generation of ABC dataset