https://github.com/ternaus/machine_learning_sign
Machine learning as a way to overcome sign problem.
https://github.com/ternaus/machine_learning_sign
Last synced: about 2 months ago
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Machine learning as a way to overcome sign problem.
- Host: GitHub
- URL: https://github.com/ternaus/machine_learning_sign
- Owner: ternaus
- License: mit
- Created: 2015-03-14T03:13:46.000Z (over 11 years ago)
- Default Branch: master
- Last Pushed: 2015-03-15T00:29:59.000Z (over 11 years ago)
- Last Synced: 2025-01-25T21:13:17.833Z (over 1 year ago)
- Language: Python
- Size: 215 KB
- Stars: 0
- Watchers: 2
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# Extrapolation to the region with a sign problem.
## Introduction
Sign problem is a fundamential problem in a theoretical condensed matter physics that pervents theorist from numerical investigation properties of the fermionic Hubbard model. There is no clear way how to measure quantities of interest in a region where average sign in the monte carlo simulations is close to zero, but I will try to use machine learning algorithms to create a model that will be able to extrapolate to the regions of interest.
Sign problem will not appear at:
* mu = 0 This corresponds to a half filled case, in which sign = 1 protected by the particle symmatric form of the Hamiltonian.
* U = 0 In this case there is no sign problem and solution to the problem can be found analytically.
In all other cases:
Sign will appear at:
* U -> infinity
* beta -> infinity
## What is my training data?
As a training set I will use output of the Determinant Monte Carlo simulations generated by QUEST package and exact diagonalization results generated by the ALPS package.
### What lattice I am working with?
In this project I will work only with the square lattice, although other lattices like honeycomb,triangular, Kagome, Lieb and others may be investigated later.
I will imply periodic boundary conditions on the lattice and I will not use lattices with sizes less than 4 in any direction.
### What are my input parameters?
As an input parameters I will use:
* Nx - Number of sites in the x direction. (even numbers only to avoid frustration)
* Ny - Number of sites in the y direction. (even numbers only to avoid frustration)
* mu - chemical potential
* beta - inverse temperature
* U - interaction strength
### What data do we have?
Exact diagonalization will give you results for any mu and U, but for (Nx, Ny) = (4, 4) and T = 0 (beta = infinity)
Quantum Monte Carlo data will be give for different U, beta, mu, Nx, Ny. Data files where < 0.1 will be considered bad (not reliable) and they will be exluded from the consideration.
### What algorithms will I use?
I am planning on using all regression algorithms from the scikit-learn package.
Comparison of their efficiency will be also provided.