Quantum Phase Transitions - Maple Application Center
Application Center Applications Quantum Phase Transitions

Quantum Phase Transitions

Author
: Jeriann Beiter
Engineering software solutions from Maplesoft
This Application runs in Maple. Don't have Maple? No problem!
 Try Maple free for 15 days!
While classical phase transitions are common phenomena widely understood on a basic level, the subject of quantum phase transitions is much less frequently broached at a pedagogical level. Here, our discussion will start with a basic introduction of the fundamental differences (and similarities) between classical and quantum phase transitions. We will introduce the Ising model as a quantitative model of phase transitions, and major results of the 1D Ising model will be briefly reviewed. Moving into applications of quantum phase transitions using the Ising model, the magnetization phase diagram of LiHoF4 will be presented, along with some of the electronic structure properties of the compound to demonstrate why it is a suitable example. Electronic structure properties, such as dipole moment, will be calculated in the worksheet using Maple. Overall, students should come away with an appreciation of using the Ising model to understand quantum phase transitions, and how this model can be applied to real systems. This worksheet uses the Maple Quantum Chemistry Toolbox.

Application Details

Publish Date: March 16, 2020
Created In: Maple 2019
Language: English

More Like This

Matrix Representation of Quantum Entangled States: Understanding Bell's Inequality and Teleportation
Quantum Mechanics: Schrödinger vs Heisenberg picture
The Gross-Pitaevskii equation and Bogoliubov spectrum
The Landau criterion for Superfluidity
Ground state of a quantum system of identical boson particles
Quantization of the Lorentz Force
Simulation on maple of the nine qubit Shor code using Feynman program
PX: A package for multiplication and commutation of quantum operators
Density of Probability of an Electron near the Nucleus