Constructing and Study of 1d And Quasi-1d Spin Models Through Matrix Product States Formalism (Mps)

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Sadrolashrafi, Afsaneh | 2010

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Type of Document: Ph.D. Dissertation
Language: Farsi
Document No: 40488 (04)
University: Sharif University of Technology
Department: Physics
Advisor(s): Karimipour, Vahid
Abstract:
Matrix Product States (MPS) is an analytical formalism to construct solvable many-body quan-tum models, which is based on the concepts of quantum information and computation theory. In this dissertation, We brieﬂy review the history of matrix product states. We follow these states from quantum Markovian states(QMS) and valence bond solid states(VBS) to ﬁnitely correlated states(FCS) and matrix product states(MPS). We then present our method of study-ing and working with MP states and we introduce and study in detail the 1D and quasi-1D solvable spin models that we have been able to successfully construct in this frame work and calculate the corresponding correlations and quantities. These spin models are a Heisenberg chain, a generalized Majumdar-Ghosh chain, and a spin ladder correspondingly
Keywords:
Finitely Correlated State ; Quantum Spin Chains ; Heisenberg Chain ; Quantum Entanglement ; Correlation Functions ; Quantum Many-body Spin System ; Quantum Spin Ladder ; Majumdar-Ghosh Chain