Tensor network states and effective particles for low-dimensional quantum spin systems

Description

This thesis develops new techniques for simulating the low-energy behaviour of quantum spin systems in one and two dimensions. Combining these developments, it  subsequently uses the formalism of tensor network states to derive an effective particle description for one- and two-dimensional spin systems that exhibit strong quantum correlations. These techniques arise from the combination of two themes in many-particle physics: (i) the concept of quasiparticles as the effective low-energy degrees of freedom in a condensed-matter system, and (ii) entanglement as the characteristic feature for describing quantum phases of matter. Whereas the former gave rise to the use of effective field theories for understanding many-particle systems, the latter led to the development of tensor network states as a description of the entanglement distribution in quantum low-energy states. Read more... Abstract: This thesis develops new techniques for simulating the low-energy behaviour of quantum spin systems in one and two dimensions. Read more... Front Matter ....Pages i-xiii Overview (Laurens Vanderstraeten)....Pages 1-4 Introduction to Quantum Many-Body Physics (Laurens Vanderstraeten)....Pages 5-57 Effective Particles in Quantum Spin Chains: The Framework (Laurens Vanderstraeten)....Pages 59-124 Effective Particles in Quantum Spin Chains: Applications (Laurens Vanderstraeten)....Pages 125-165 Towards a Particle Theory in Two Dimensions (Laurens Vanderstraeten)....Pages 167-202 Back Matter ....Pages 203-219