A quantum spin system is a lattice where spins are fixed on different discrete lattice points. The interaction of the spins is kept local, in the sense that it is usually restricted to nearest neighbor and next nearest neighbor interactions.

Although these spin Hamiltionians are quite simple and easily formulated, their behavior can be all but trivial and numerous phases and phase transitions may occur. These systems are not only interesting due to their emergent properties, but are also actively used for modeling real magnetic materials.

One of the possible types of phases in a quantum spin lattice system is the so-called quantum spin liquid, “liquid” referring to its disordered nature in contrast with ordered (anti-)ferromagnetic phases. Spin-liquid states can be used for topological quantum computing and are useful for the research of high temperature superconductivity. Because of this, understanding this spin-liquid state and finding materials showing this phase is a hot topic.

Due to the curse of dimensionality, exactly solving arbitrary spin lattice systems is only possible for a small number of spins. To find the phase diagram one has to be able to solve very large systems, approaching the thermodynamic limit. Approximate solution methods are therefore needed.

Different approximate methods have been used for the study of these systems like:
• spin-wave theory,
• Quantum Monte Carlo,
• coupled cluster method,
• cluster density matrix embedding theory,
• and tensor network states as density matrix embedding theory and projected entangled pair states.

For many systems there is still no agreement on the location of the phase transitions or even on the exact nature of the emerging phases, making it a very active field of study.

Goal

The goal of this thesis is to study different quantum spin systems through the use of approximate methods. Depending on the student's interest, he/she will develop his/her own code in a language of choice or improve and expand already existing in-house code. This involves learning different concepts and techniques used in many-body quantum physics, understanding the consequences of the approximations made and learning how to efficiently implement computationally intensive code.

The student would benchmark his/her code on exactly solvable systems as a first step, later moving on to the study of other systems where the quantum phase diagram is still unknown and highly desirable.

Aspect

The engineering aspect of this thesis concerns the efficient implementation for the modeling of magnetic materials, which have their usefulness in quantum computing and high temperature superconductivity.

This research topic will be conducted in the framework of a strong international network and if possible the student will be actively involved in work discussions with collaborative partners.