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

GitHub saver for stargazers, forks, repos

Python script for changing the SSH banner content with other content

:fishing_pole_and_fish: List of `pre-commit` hooks to ensure the quality of your `dbt` projects.

This is some simple code to scrape vistbook's system to get an overview of the different cabins availability.

World's best free and open source ERP.

A project to explore and provide useful code for Mango Markets

Python package that mirrors the original Nodejs ReplAPI-It.

DC619/DC858 Mainframe Environment/Lab

WhyNotWin11 - Detection Script to help identify why your PC isn't Windows 11 Release Ready

Python library to natively send files to Trash (or Recycle bin) on all platforms.

Imports an object based on a string import_string('package.module:function_name')() - Based on werkzeug.utils

Monitor the New World login queue and notify when it is about to finish

python package to showcase, test and build your own version of Pickhardt Payments

little proyect to organize myself, but maybe can help someone else

PhD document for navlab

Old versions of Deadcord that are problematic or used as reference.

1cak - An Indonesian web that provide lot of fun.

Combines power of torch, numerical methods to conquer and solve ALL {O,P}DEs

Modern API wrapper for Genshin Impact built on asyncio and pydantic.

A web application which you can search, buy or sell shares with current prices which provided by IEX.