https://www.amazon.com/dp/0521514681/?tag=pfamazon01-20nik9039 said:Trying to understand what the math methods are exist to determine quantum phase transition and how I can calculate it, by what methods.
A quantum phase transition is a phenomenon that occurs in certain materials at extremely low temperatures, where small changes in external conditions (such as pressure or magnetic field) can cause a sudden and dramatic change in the material's physical properties. This transition is driven by quantum mechanical effects and can result in changes in the material's magnetic, electrical, or structural properties.
In a classical phase transition, such as melting or boiling, the change in physical properties is caused by thermal energy. In a quantum phase transition, the change is driven by quantum fluctuations, which are inherent in the quantum nature of matter. These fluctuations are present even at absolute zero temperature and can cause sudden changes in the material's properties.
Some examples of materials that exhibit quantum phase transitions include superconductors, superfluids, and magnetic materials such as spin liquids and antiferromagnets. These materials often have unique properties at extremely low temperatures and can undergo dramatic changes in response to small changes in external conditions.
Scientists study quantum phase transitions by using techniques such as neutron scattering, nuclear magnetic resonance (NMR), and various spectroscopic methods. These techniques allow them to observe the changes in a material's physical properties and understand the underlying quantum mechanical processes driving the transition.
Quantum phase transitions have the potential to be used in various technological applications, such as in quantum computing and quantum sensors. By understanding and controlling these transitions, scientists may be able to develop new materials with unique properties that could be used in advanced technologies.