A Review on Spin Systems with Cluster-Type Interactions

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Dabiri, Sajad | 2017

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 50958 (04)
University: Sharif University of Technology
Department: Physics
Advisor(s): Langari, Abdollah
Abstract:
The aim of this thesis is to review the spin systems with cluster-type inter-actions. We restrict our attention to one dimentional and exactly solvable models. By "exactly solvable models",we mean the systems which can be mapped to free fermionic systems by Jordan-Wigner transformation.In 2nd chapter we introduce one of the simplest spin systems with cluster-type intraction, the cluster Ising model, and completely derive its statis-tics[10].In chapter 3, we present a classification of topologic phases which can oc-cur in free fermionic gapped systems. This classification is based on sym-metries. Also we'll see that with the help of topological invariants, one can diagnose different topological phases[16,17].In chapter 4 we introduce series of exactly solvable spin systems. After-ward, we study some spin models which have been considered in articles, and determine different phases of them. We'll find out that such systems can have various topological phases[19,20,23]
Keywords:
Topological phase ; Quantum Many-body Spin System ; Quantum Phase Transition

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