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

Overview

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

DOI

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.
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.
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

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

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

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

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

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

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

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

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.

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

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

A free and open-source chess improvement app that combines the power of Lichess and Anki. Chessli Project Activity & Issue Tracking PyPI Build & Healt

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

HPomb v2020.02 Coming Soon Created By Secanonm HPomb Is Socail Engineering Tool , Used For Bombing , Spoofing and Anonymity Available For Linux And An

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

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)
Owner
Joana Fraxanet
Joana Fraxanet
With the initiation of the COVID vaccination drive across India for all individuals above the age of 18, I wrote a python script which alerts the user regarding open slots in the vicinity!

cowin_notifier With the initiation of the COVID vaccination drive across India for all individuals above the age of 18, I wrote a python script which

13 Aug 01, 2021
A pairs trade is a market neutral trading strategy enabling traders to profit from virtually any market conditions.

A pairs trade is a market neutral trading strategy enabling traders to profit from virtually any market conditions. This strategy is categorized as a statistical arbitrage and convergence trading str

Kanupriya Anand 13 Nov 27, 2022
JupyterLite as a Datasette plugin

datasette-jupyterlite JupyterLite as a Datasette plugin Installation Install this plugin in the same environment as Datasette. $ datasette install dat

Simon Willison 11 Sep 19, 2022
String Spy is a project aimed at improving MacOS defenses.

String Spy is a project aimed at improving MacOS defenses. It allows users to constantly monitor all running processes for user-defined strings, and if it detects a process with such a string it will

10 Dec 13, 2022
Groupe du projet Python en 2TL2-4

Présentation Projet EpheCom Ce logiciel a été développé dans le cadre scolaire. EpheCom est un logiciel de communications - vocale et écrite - en temp

1 Dec 26, 2021
Project Faros is a reference implimentation of Red Hat OpenShift 4 on small footprint, bare-metal clusters.

Project Faros Project Faros is a reference implimentation of Red Hat OpenShift 4 on small footprint, bare-metal clusters. The project includes referen

project: Faros 9 Jul 18, 2022
An experimental Python-to-C transpiler and domain specific language for embedded high-performance computing

An experimental Python-to-C transpiler and domain specific language for embedded high-performance computing

Andrea Zanelli 562 Dec 28, 2022
Daily knowledge pills to get better in Python.

Python daily pills Daily knowledge pills to get better Python code. Why Does your Python code suffers of any of this symptoms? Incorrect Indentation I

Jeferson Vaz dos Santos 35 Sep 19, 2022
NUM Alert - A work focus aid created for the Hack the Job hackathon

Contributors: Uladzislau Kaparykha, Amanda Hahn, Nicholas Waller Hackathon Team Name: N.U.M General Purpose: The general purpose of this program is to

Amanda Hahn 1 Jan 10, 2022
🔵Open many google dorks in a fasted way

Dorkinho 🔵 The author is not responsible for misuse of the tool, use it in good practices like Pentest and CTF OSINT challenges. Dorkinho is a script

SidHawks 2 May 02, 2022
Материалы для курса VK Углубленный Python, весна 2022

VK Углубленный Python, весна 2022 Материалы для курса VK Углубленный Python, весна 2022 Лекции и материалы (слайды, домашки, код с занятий) Введение,

10 Nov 02, 2022
Open source style Deep Dream project

DeepDream ⚠️ If you don't have a gpu with cuda, the style transfer execution time will be much longer Prerequisites Python =3.8.10 How to Install sud

Patrick martins de lima 7 May 17, 2022
Run Python code right in your Telegram messages

Run Python code right in your Telegram messages Made with Telethon library, TGPy is a tool for evaluating expressions and Telegram API scripts. Instal

29 Nov 22, 2022
The LiberaPay archive module for the SeanPM life archive project.

By: Top README.md Read this article in a different language Sorted by: A-Z Sorting options unavailable ( af Afrikaans Afrikaans | sq Shqiptare Albania

Sean P. Myrick V19.1.7.2 1 Aug 26, 2022
Reconhecimento de voz, em português, com python

Speech_recognizer Reconhecimento de voz, em português, com python O ato de falar nada mais é que criar vibrações no ar. Por meio de um conversor analó

Marcus Vinícius Ribeiro Andrade 1 Dec 14, 2021
Video Stream is an Advanced Telegram Bot that's allow you to play Video & Music on Telegram Group Video Chat

Video Stream is an Advanced Telegram Bot that's allow you to play Video & Music on Telegram Group Video Chat 📊 Stats 🧪 Get SESSION_NAME from below:

dark phoenix 12 May 08, 2022
Multi-Probe Attention for Semantic Indexing

Multi-Probe Attention for Semantic Indexing About This project is developed for the topic of COVID-19 semantic indexing. Directories & files A. The di

Jinghang Gu 1 Dec 18, 2022
A class to draw curves expressed as L-System production rules

A class to draw curves expressed as L-System production rules

Juna Salviati 6 Sep 09, 2022
A numbers check python package

A numbers check python package

Fayas Noushad 3 Nov 28, 2021
End-to-End text sumarization, QAs generation using flask.

Help-Me-Read A web application created with Flask + BootStrap + HuggingFace 🤗 to generate summary and question-answer from given input text. It uses

Ankush Kuwar 12 Nov 13, 2022