Quantum Phase Transitions and Emergent Phases in Ladder Systems

Abstract

This thesis investigates the ground-state properties and quantum phase diagrams of low-dimensional spin systems, with a focus on spin–1/2 ladder chains and related models.

These systems provide a fertile ground for exploring the interplay between magnetic frus- tration, quantum correlations, topology, and external fields. By combining advanced nu- merical methods, primarily the density matrix renormalization group (DMRG), with ana- lytical approaches, we analyze how different coupling geometries and magnetic fields give

rise to distinct quantum phases, including magnetization plateaus, symmetry-protected and topological phases, and first-order transitions. The study covers both uniform and alternating ladders, as well as coupled ladder systems that interpolate between one- and

two-dimensional behavior. In particular, we examine how frustration influences the stabil- ity of collective spin states, and how interladder couplings can drive transitions between

resonating valence bond (RVB) states, Haldane phases, and trivial phases hosting collec- tive spin excitations. Although approximate analytical models, such as hard-core boson

mappings and spin-wave theory, capture some qualitative aspects of these systems, our results highlight their limitations in accurately describing critical behavior and phase boundaries, reinforcing the importance of high-precision numerical analysis.