Diagonalizing Quantum Spin Chains

Bachelor thesis (2015)
Copyright: © 2015 Slooter, R.J.
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Published Date

03-07-2015

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Abstract

The goal of this research project is to study spin chains. This involves diagonalizing large matrices. These largematrices are theHamiltonian matrices of the quantumspin chains. So the eigenvalues represent energy values. Before going into the actual programming it is important to understand how the Hamiltonian works, and how the quantum spin chain is modeled. The first case studied is a static spin-12 system, for this system we want to know the lowest eigenvalues this will be done using the Lanczos algorithm. Once the static case is solved it is possible to extend the system with a variable magnetic field. The goal is to optimize this program, therefore we take a look at possible improvements. Another topic is the seemingly critical behavior of the system, for this the critical exponents are determined. Finally we will look into the DensityMatrix Renormalization Group (DMRG) method.