Project R-16790

Modulated structures in quantum spin chains (Research)

This PhD project investigates modulated structures in quantum spin chains, focusing on how competition between interactions and aperiodic order affects quantum phase transitions and excited states. The work is divided into two main parts. The first part studies the quantum ANNNI (axial next-nearest-neighbor Ising) chain in a transverse field. This model exhibits frustration and complex modulated phases. The goal is to analyze quantum phase transitions using entanglement measures, particularly the von Neumann entropy, and to extend previous small-system studies to much larger system sizes using matrix product state techniques. The second part examines aperiodic spin chains, where deterministic but nonperiodic modulations of the couplings can strongly affect the system's properties. In particular, the project aims to investigate the emergence of effective dimerization and energy gaps, especially in excited states, using strong-disorder renormalization-group methods and density-matrix renormalization-group calculations. The results may contribute to understanding interaction-driven localization phenomena and could have implications for robust quantum memory design. Overall, the project combines analytical and advanced numerical methods to explore how frustration, aperiodicity, and interactions shape the ground and excitedstate properties of low-dimensional quantum systems.

18 June 2026 - 30 September 2029