Kvantové stavy reprezentované neuronovýmí sítěmi pro systémy v magnetickem poli
| Název práce v češtině: | Kvantové stavy reprezentované neuronovýmí sítěmi pro systémy v magnetickem poli |
|---|---|
| Název v anglickém jazyce: | Neural network quantum states for systems in magnetic field |
| Klíčová slova: | Kvantové stavy reprezentované neuronovýmí sítěmi|NetKet|Kvantový magnetismus |
| Klíčová slova anglicky: | Neural network quantum states|NetKet|Quantum magnets |
| Akademický rok vypsání: | 2023/2024 |
| Typ práce: | diplomová práce |
| Jazyk práce: | |
| Ústav: | Katedra fyziky kondenzovaných látek (32-KFKL) |
| Vedoucí / školitel: | RNDr. Martin Žonda, Ph.D. |
| Řešitel: |
| Zásady pro vypracování |
| What will student learn:
Standard and nonstandard machine learning techniques with the stress on deep learning. Neural network package NetKet Basics of many-body physics Basics of quantum Monte Carlo What will student do: Building neural network architectures for quantum many-body systems in magnetic field Setting and running variational quantum Monte Carlo simulations |
| Seznam odborné literatury |
| F Vicentini et al., NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems, SciPost (2022)
P. Mehta et al: A High-Bias, Low-Variance Introduction to Machine Learning forPhysicists, Physics Reports810, 1 (2019) G. Carleoet al.: Machine learning and the physical sciences, Rev. Mod. Phys. 91, 045002 (2019) L. Zdeborová: Understanding deep learning is also a job for physicists, Nature Physics 16, 602 (2020) |
| Předběžná náplň práce v anglickém jazyce |
| Very recently a new field emerged in physics where we investigate the possibility to represent many-body wave-functions by neural-network states. The main motivation behind this idea is that a sufficiently complex neural network is a so called general approximator. This means that, in theory, it can represent any smooth enough function. It had been already shown that neural networks can be used to calculate the ground state of several quantum spin models. However, all so far published results have focused on zero magnetic field. Yet, for many systems, including the so-called Shastry Sutherland magnets the interesting physics happens when the magnetic field is present. It can lead to exotic phases of matter and strange phase transitions, as well as surprisingly stable regimes. We have already tested the usually used neural network techniques and found out that they do not work in finite magnetic field. The challenging task for the student would be to solve this problem. |