Authors:	Kshetrimayum, Augustine
Title:	Quantum many-body systems and Tensor Network algorithms
Online publication date:	27-Apr-2018
Year of first publication:	2018
Language:	english
Abstract:	Theory of quantum many-body systems plays a key role in understanding the properties of phases of matter found in nature. Due to the exponential growth of the dimensions of the Hilbert space with the number of particles, quantum many-body problems continue to be one of the greatest challenges in physics and most of these systems are impossible to study exactly. We therefore need efficient and accurate numerical algorithms to understand them. In this thesis, we exploit a new numerical technique known as Tensor Network algorithms to study exotic phases of matter in three different investigations in one and two spatial dimensions. In the first part, we use Matrix Product States which is a one-dimensional ansatz of the Tensor Network family to study trivial and topological phases of matter protected by symmetries in a spin-2 quantum chain. For this, we investigate a Heisenberg-like model with bilinear, biquadratic, bicubic and biquartic interactions with an additional uniaxial anisotropy term. We also add a staggered magnetic field afterwards to break the symmetries protecting the topological phases and study their ground state properties. In the second part of the thesis, we use Tensor Network States in 2D known as Projected Entangled Pair States to study frustrated quantum systems in a kagome lattice, more specifically, the XXZ model. We study the emergence of different magnetization plateaus by adding an external magnetic field and show the delicate interplay between the number of unit cells and the symmetry of the ground state. Finally, we propose an algorithm based on Tensor Networks to study open dissipative quantum systems in 2D. We then use it to investigate the spin-1/2 Ising and the XYZ model in a square lattice, both of which can be realized experimentally using cold Rydberg atoms.
DDC:	530 Physik 530 Physics
Institution:	Johannes Gutenberg-Universität Mainz
Department:	FB 08 Physik, Mathematik u. Informatik
Place:	Mainz
ROR:	https://ror.org/023b0x485
DOI:	http://doi.org/10.25358/openscience-2659
URN:	urn:nbn:de:hebis:77-diss-1000019726
Version:	Original work
Publication type:	Dissertation
License:	In Copyright
Information on rights of use:	https://rightsstatements.org/vocab/InC/1.0/
Extent:	x, 174 Seiten
Appears in collections:	JGU-Publikationen